# Mathematics Colloquium Archive

The following are the Mathematics Colloquia from previous semesters.

## Spring 2023

Shiyun Wang, USC

### Abstract

This talk presents my collaborative work that extends the current investigations on the (3+1)-free posets conjectures by Stanley-Stembridge and Shareshian-Wachs with the q-parameterized version. We expand the chromatic symmetric functions for Dyck paths of bounce number three in the elementary symmetric function basis using a combinatorial interpretation of the inverse of the Kostka matrix studied in Egecioglu-Remmel (1990). We construct sign-reversing involutions to prove that certain coefficients in this expansion are positive. We use a similar method to establish the e-positivity of chromatic symmetric functions for Dyck paths of bounce number three beyond the “hook-shape” case of Cho-Huh (2019). Our results provide more supportive evidence for the Stanley-Stembridge Conjecture by extending the e-positive class of the incomparability graph of natural unit interval orders.

### Bio Sketch

Shiyun Wang's educational background includes a B.A. in management from Central South University in China, a Master of Public Administration from the University of Southern California (USC), and an M.S. in Mathematics from California State University Long Beach (CSULB). She is a Ph.D. candidate in mathematics at USC and will join the University of Minnesota as a postdoc this fall. Shiyun has developed research interests in algebraic and enumerative combinatorics, tableaux combinatorics, symmetric functions, and quasi-symmetric functions in relation to representation theory. Her current work focuses on chromatic quasisymmetric functions and row-strict dual immaculate functions with connections to 0-Hecke algebra.

Dr. Cash Bortner, CSU Stanislaus

### Abstract

Since Recovering parameter values from mathematical models is a primary interest of those that use them to model the physical and biological world. This recovery, or identification, of parameters within models is also an interesting mathematical problem that we call Identifiability. In this talk, we will explore the identifiability of a specific type of model called Linear Compartmental Models, which are often used to understand biological phenomena and have an underlying graphical structure. Starting with an introduction to graph theory, we will explore the relationship that this graphical structure has to Linear Compartmental Models and their defining differential equations. At the end of the talk, we classify identifiability criteria for an interesting subclass of Linear Compartmental Models called tree models.

Dr. Yat Sun Poon, UC Riverside

### Abstract

Since the success of Nomizu in 1954 in showing that the DeRham cohomology on compact nilmanifolds are given by invariant differential forms, there have been many attempts to accomplish the same on various cohomology theories on compact complex manifolds. After a brief review of such accomplishments, we focus on the role of abelian complex structures in both the classical and modern perspectives. Our goal is to present a few issues for consideration within the realm of Hitchin's generalized geometry, a geometry that encompass both complex and symplectic structures.

### Bio Sketch

Dr. Yat Sun Poon obtained his Ph.D. degree from Oxford University in 1985 under the direction of Dr. Nigel Hitchin. Dr. Poon's research program anchors in mathematical physics as developed by Atiyah, Hitchin, and Penrose, especially on quantum gravity, twistor theory, monopole, and string theory. In recent years, his research focus is on the deformation theory of generalized comple geometry. He is currently an editor for the journal Complex Manifolds.

Since joining UC Riverside in 1991, Dr. Poon has served as the Associate Dean of Physical and Mathematical Sciences, College of Natural and Agricultural Sciences, UC Riverside and the chair of the Department of Mathematics at UC Riverside. Besides of research, Dr. Poon has devoted much effort in undergraduate education including effort in articulation with the full spectrum of K-16 public institutions. He was the director and producer of the UCR's Micro-tutorial in Mathematics from 2015 to 2020 supported by UCR Provost's Office. Since 2021, he collaborates with his colleagues in the Department of Mathematics and School of Education to advance A New Mathematics Gateway, a program funded by the California Learning Lab.

Dr. Pei-Ken Hung, University of Minnesota

### Abstract

In this presentation, I will provide an overview of geometric analysis, including major breakthroughs in this field over the past few decades and how partial differential equations (PDEs) were used to solve them. We will explore how the three types of PDEs (elliptic, parabolic, and hyperbolic) arise in various problems. Lastly, I will discuss my work in each of these three categories.

### Bio Sketch

Pei-Ken Hung is a mathematician in the field of geometric analysis and general relativity. He is an assistant professor at the University of Minnesota. Dr. Hung earned a doctorate in mathematics from Columbia University in 2018, under the supervision of Mu-Tao Wang and Simon Brendle. Before joining the University of Minnesota, Dr. Hung has worked at MIT as the C.L.E. Moore Instructor.

Dr. Cristian Oliva-Aviles, Genentech

### Abstract

Biostatisticians play a key role throughout the lifecycle of drug development. They actively collaborate with several functions to design research studies, and to collect and analyze the data needed to draw conclusions about the safety and efficacy of a new drug molecule. Since clinical trials are generally designed to answer a specific question regarding a medical product, there cannot be clinical trials without drug molecules to test. In this talk, an overview of Genentech and its Data Sciences organization will be presented. In addition, the complexity of consistently manufacturing high-quality drugs will be shown to motivate the critical role that nonclinical biostatisticians play during the pharmaceutical drug development process.

### Bio Sketch

Cristian has worked as a statistical scientist in the department of Pharmaceutical Development at Genentech since 2018, where he has been a member of the Nonclinical Biostatistics team. He was the coordinator of the 2022 Data & Statistical Sciences Summer Internship Program at Genentech. Cristian is a mathematician with a Ph.D. in Statistics from Colorado State University, with expertise in the areas of shape-restricted regression and survey sampling. The one thing Cristian enjoys the most of being a statistician is collaborating in multidisciplinary projects.

Dr. Xiangwen Zhang, UC Irvine

### Abstract

Geometric flows have been proven to be powerful tools in the study of many important problems arising from both geometry and theoretical physics. Aiming to study the equations from the flux compactifications of Type IIA superstrings, we introduce the so-called Type IIA flow, which is a flow of closed and primitive 3-forms on a symplectic Calabi-Yau 6-manifold. Remarkably, the Type IIA flow can also be viewed as a flow as a coupling of the Ricci flow with a scalar field. In this talk, we will discuss the recent progress on this flow.

### Bio Sketch

Xiangwen Zhang is an associate professor at UC Irvine, working in the field of geometric analysis and non-linear PDEs. Before joining UC Irvine, he was a Ritt Assistant Professor at Columbia University.

Gary Green, The Aerospace Corporation; SIAM Visiting Lecturer

### Abstract

The Boeing Inertial Upper Stage (IUS) carried spacecraft from low earth orbits to their mission orbits from 1982 until 2004. Gamma Guidance provided the means of controlling the rocket engine firings in the presence of irregularities so that the spacecraft were injected into their desired orbits. I will discuss the basics of Gamma Guidance as well as selected collateral mathematics topics required for IUS success. Boeing analysts applied a number of techniques to solve a variety of problems in the face of challenging obstacles.

Nicholas Marco, UCLA

### Abstract

Mixed membership models, or partial membership models, are a flexible unsupervised learning method that allows each observation to belong to multiple clusters. In this talk, we propose a Bayesian partial membership model for functional data. By using the multivariate Karhunen-Loève theorem, we are able to derive a scalable representation of Gaussian processes that maintains data-driven learning of the covariance structure. Compared to previous work on mixed membership models, our proposal allows for increased modeling flexibility, with the benefit of a directly interpretable mean and covariance structure. Our work is motivated by studies in functional brain imaging through electroencephalography (EEG) of children with autism spectrum disorder (ASD). In this context, our work formalizes the clinical notion of "spectrum" in terms of feature membership proportions.

### Bio Sketch

Nicholas Marco is currently a 5th year Ph.D. student in the department of Biostatistics at UCLA, under the supervision of Donatello Telesca. His primary research focuses on Bayesian Methods for functional data analysis, applied to the field of neuroscience. Nicholas also collaborates with the Jonsson Comprehensive Cancer Center to create microRNA-based biomarkers to personalize cancer treatment. Prior to joining UCLA, Nicholas graduated from California State University, Long Beach in 2017 with a Bachelor of Science degree in Mathematics with an option Statistics.

Dr. Guofang Wei, UC Santa Barbara

### Abstract

The fundamental (or mass) gap refers to the difference between the first two eigenvalues of the Laplacian or more generally for Schrödinger operators. It is a very interesting quantity both in mathematics and physics as the eigenvalues are possible allowed energy values in quantum physics. In their celebrated work, B. Andrews and J. Clutterbuck proved the fundamental gap conjecture that difference of first two eigenvalues of the Laplacian with Dirichlet boundary condition on convex domain with diameter D in the Euclidean space is greater than or equal to 3π^{2}/D^{2}. In several joint works with X. Dai, Z. He, S. Seto, L. Wang (in various subsets) the estimate is generalized, showing the same lower bound holds for convex domains in the unit sphere. In sharp contrast, in recent joint work with T. Bourni, J. Clutterbuck, X. Nguyen, A. Stancu and V. Wheeler (a group of women mathematicians), we prove that there is no lower bound at all for the fundamental gap of convex domains in hyperbolic space in terms of the diameter. Very recently, jointed with X. Nguyen, A. Stancu, we show that even for horoconvex (which is much stronger than convex) domains in the hyperbolic space, the product of their fundamental gap with the square of their diameter has no positive lower bound. All necessary background information will be introduced in the talk.

### Bio Sketch

Guofang Wei is a mathematician in the field of differential geometry and geometric analysis. She is a professor at the University of California, Santa Barbara. Professor Wei earned a doctorate in mathematics from the State University of New York at Stony Brook in 1989, under the supervision of Detlef Gromoll. In 2013, she became a fellow of the American Mathematical Society, for "contributions to global Riemannian geometry and its relation with Ricci curvature."

The research of Professor Wei has been concentrated on global Riemannian geometry--the interaction of curvature with the underlying geometry and topology which includes the study of the fundamental groups, comparison geometry, manifolds with integral curvature bounds, spaces with weak curvature bounds, the eigenvalue of Laplacian, and more.

## Fall 2022

Dr. Siqi Fu, Rutgers University, Camden

### Abstract

In this expository talk, I will discuss the several complex variables analogue of Mark Kac's question "Can One Hear the Shape of a Drum?": To what extent can one determine geometric properties of a domain in several complex variables from spectral properties of the complex Neumann Laplacian? I will explain that one can detect more geometric properties with the complex Neumann Laplacian than the classical Dirichlet or Neumann Laplacian.

### Bio Sketch

Dr. Siqi Fu is a Professor and the Chair of the Department of Mathematical Sciences at Rutgers University, Camden. He received his Ph.D. degree in Mathematics from Washington University in St. Louis under the supervision of Steven George Krantz. Professor Fu was a recipient of an American Mathematical Society Centennial Research Fellowship in 2000.

Dr. Fu's research interest is spectral analysis of partial differential operators and geometric analysis in several complex variables. The basic theme is to study the interplay among geometric, analytic, and algebraic structures of a complex manifold.

Dr. Jessi Lajos, Colorado State University

### Abstract

In this descriptive case study, we explored how an embodied cognition researcher integrated embodiment beyond gesture as she taught a first semester abstract algebra course. We found that this instructor intentionally used embodiment to motivate and ground formal definitions, theorems, and proofs. In addition to her use of gesture, she encouraged students to interact with physical materials and simulate the mathematics with their bodies. Simulations opened communication lines between the instructor and students, who were not fluent in formal language. Furthermore, the instructor's simultaneous use of various forms of embodiment highlighted and disambiguated referents of student's speech, positioned students' contributions as legitimate, and carried forth students' theories. Our results offer practical implications for teaching by illustrating examples of how embodiment can be incorporated into an abstract algebra classroom.

### Bio Sketch

Dr. Jessi Lajos is a postdoctoral scholar at Colorado State University, specializing in undergraduate abstract algebra education.

Dr. Jim Stein, CSU Long Beach

11/8/2022 Presentation Slides (PDF)

### Abstract

This talk will explore three related problems in probability in which a simple technique can be used to improve one's chances of making the correct guess in what initially appears to be a 50-50 situation. The talk can be understood by anyone familiar with the fact that for two independent events A and B, P(AnB) = P(A)P(B) -- and even if you're not familiar with that there's better than a 50-50 chance you will enjoy the talk.

#### Problem I - Blackwell's Bet

You have two envelopes with differing sums of money. You open one of them, look at the amount of money in it, and are offered the following choice - you can either keep the money in the opened envelope, or take the money in the unopened envelope. There's a really cute and simple technique, often ascribed to David Blackwell, of making your choice in such a way that you have better than a 50-50 chance of choosing the larger of the two amounts.

#### Problem II - A Stop at Willoughby

This is the title of an episode of the Twilight Zone TV series, You go to sleep on a train which is moving via a random walk along an east-west line. When you wake up, you are stopped at a station and hear the conductor say, "Next stop, Willoughby." A simple variation of the technique described in Blackwell's Bet enables you to have better than a 50-50 chance of guessing whether Willoughby is to the east or the west.

#### Problem Ill - ????

A mystery problem which has yet to be fully resolved, but which has better than a 50-50 chance of piquing your curiosity.

### Bio Sketch

Jim Stein is an Emeritus Professor of Mathematics at CSU Long Beach. The word 'emeritus' comes from the Latin 'ex', meaning 'out', and 'meritus', meaning 'ought to be'.

Dr. Alexandre Girouard, Université Laval

### Abstract

It has been known since classical antiquity that disks have the largest area among planar figures of prescribed perimeter. Nevertheless, a complete proof was only given around the end of the 19th century! During the 20th century, area and perimeter were replaced by several new analytic and geometric quantities, such as the heat content, torsional rigidity and natural frequencies of vibrations. In this talk, I will survey recent results on isoperimetric bounds for eigenvalues of Laplace type operators and their generalizations. I will stress in particular some recent joint work with Mikhail Karpukhin and Jean Lagace, in which we given a complete solution for the isoperimetric problem associated to the eigenvalues of the Dirichlet-to-Neumann maps on planar domains and surfaces. The DtN map is in itself a very interesting object, which arise from the study of inverse problems that are linked to geophysical and medical imaging. The first half of the talk will be accessible to undergraduate students.

### Bio Sketch

Alexandre Girouard is a math professor at Universite Laval, in Quebec city. He received his Ph.D at Universite de Montreal under the supervision of losif Polterovich and Marlene Frigon. He has worked at Cardiff School of Mathematics as Postdoc, Institute of Mathematics of Neuchatel as Assistant Professor and University of Savoie as lecturer, before joining Laval University in 2013. Professor Girouard's research area is the spectral geometry. He is interested in isoperimetric type problems for the eigenvalues of the Laplacian and the Drichlet-Neumann operator on Riemannian manifolds.

Xiaoming Xu, Duke University

### Abstract

Clinical trials of many chronic diseases such as Parkinson's disease often collect multiple health outcomes to monitor the disease severity and progression. It is of scientific interest to test whether the experimental treatment has an overall efficacy on the multiple outcomes across time, as compared to placebo or an active control. To compare the multivariate longitudinal outcomes between two groups, the rank-sum test and the variance-adjusted rank-sum test can be used to test the treatment efficacy. But these two rank-based tests, by utilizing only the change from baseline to the last time point, do not fully take advantage of the multivariate longitudinal outcome data, and thus may not objectively evaluate the global treatment effect in the whole therapeutic period. In this paper, we develop a longitudinal rank-sum test to detect global treatment efficacy in clinical trials with multiple longitudinal outcomes. Asymptotic properties of the proposed global test procedure are derived and thoroughly examined. Simulation studies under various scenarios are performed. The test statistic is motivated by and applied to a recently completed randomized controlled trial of Parkinson's disease.

### Bio Sketch

Dr. Xu's research interests lie primarily in survey statistics, shape restricted estimation and inference, and non-parametric statistical methods in longitudinal studies. He is currently working on developing novel statistical methods to solve real statistical problems in longitudinal studies. Particularly, he is developing a nonparametric test for multivariate longitudinal outcomes in clinical trials. Dr. Xu current works as a postdoctoral associate at the department of biostatistics and bioinformatics, Duke University.

Dr. Nancy Kress, University of Colorado, Boulder

### Abstract

A brief introduction and overview of critical pedagogy will provide a jumping off point for explaining key constructs of equitable mathematics instruction. I will describe the pedagogical perspectives and instructional practices held and used by instructors at two different large Hispanic Serving Institutions who were identified as especially committed to equitable and inclusive instruction.

Experiences of these learning contexts from instructor and student perspectives will be shared. I will return to the tenets of critical pedagogy to propose how dialogue may serve as an overarching theme to guide us in the teaching of mathematics in ways that welcome and reflect more diverse perspectives and experiences.

### Bio Sketch

Nancy Kress is an assistant teaching professor in Mathematics Education at the University of Colorado Boulder. Her dissertation focused on equitable mathematics instruction in undergraduate mathematics departments at two large minority serving institutions. Her ongoing research agenda aims to increase implementation of strategies that improve learning experiences for students who identify as members of underserved groups in mathematics. Nancy was a high school mathematics teacher for twenty years, and she has taught both mathematics and education courses at the undergraduate level.

Dr. Song-Ying Li, UC Irvine

### Abstract

In this talk, I will give a short survey on the existence and regularity theory for solutions of Cauchy-Riemann equations in a bounded domains in **C**^{n}. I will introduce the Hörmander's weighted *L*^{2} estimates for Cauchy-Riemann operator. Vanishing theorem for Cauchy-Riemann operator, sup-norm estimates for the solutions, as well as some application of the theory.

### Bio Sketch

Professor Song-Ying Li received his Ph.D. degree from University of Pittsburgh in 1992. He has been a visiting assistant professor at UC Irvine and Washington University, St. Louis. He rejoined UC Irvine in 1996, and has been an assistant professor, associate professor and full professor there. His major research interests are Several Complex Variables, Harmonic Analysis and Nonlinear Partial Differential Equations. He has received the ISSAC award and Faculty Career Development award.

Juan Diego Mejia Becerra, M.S., UC Santa Barbara

### Abstract

Colombia has a publicly funded health insurance program that aims to have universal coverage known as *Sistema General de Seguridad en Social en Salud (SGSSS)* that is regulated by the law 100 of 1993 (Lonono and Frenk, (1997). The Colombian population benefits from a fundamental right to health enshrined in the Colombian constitution which, according to the constitutional court of Colombia (statutory law 1751 of 2015), entitles the enrollees to be provided with health services and technologies on a comprehensive basis. Coverage is provided via insurers (EPSs) with reimbursement from the Colombian government according to an age/sex/geographic risk adjustment system (described in Duncan (2018)).

As with many countries this entitlement to coverage causes budgetary problems. The Colombian Health Ministry (*Ministerio de Salud*) retained Santa Barbara Actuaries Inc. to develop a new condition-based risk adjustment system with the intent of controlling spending and more equitably distributing revenue based on member need. In this presentation we discuss our modeling process and the resulting risk adjustment system.

### Bio Sketch

Juan Diego Mejia Becerra is a Ph.D. candidate in the Department of Statistics and Applied Probability at the University of California, Santa Barbara and an Associate at Santa Barbara Actuaries Inc. They hold a Master's degree from National University, Colombia.

Dr. Li-Sheng Tseng, UC Irvine

### Abstract:

Smooth functions and their generalizations, called differential forms, encode data that can be used to distinguish different geometric objects. Using only multivariable Calculus, I will motivate how we can extract some of these data by means of a standard tool of modern day geometry, known as de Rham cohomology theory. In recent years, applications of this technique have led to the revelation of new characteristic properties for a special class of geometrical spaces that are studied in mathematical physics.

### Bio Sketch

Dr. Li-Sheng Tseng is a math professor in UC Irvine. He received his bachelor's degree from Harvard University and his PhD from the University of Chicago. His recent research has focused on developing some novel cohomologies of differential forms as new tools for analyzing symplectic manifolds. He is also interested in applications of geometrical structures to theoretical physics. Dr. Tseng is a co-founder of the UC Irvine Math CEO (Community Educational Outreach) afterschool program which work with underserved middle and high school students in Southern California.

Dr. Zachary Weller, Pacific Northwest National Lab

### Abstract

Nuclear safeguards are a set of technical measures used by the International Atomic Energy Agency (IAEA) to provide credible assurance that States do not misuse material or facilities to make nuclear explosives. At the core of these technical measures are nuclear material accountancy measures, which include verification measurements of material inventory and changes. This talk will explore the role of statistics in designing verification surveys and evaluating the resulting data. Verification surveys are designed by considering the goal quantity of material to be detected, the desired probability of detection, and the performance of the measurement instruments to be used in the survey. We will demonstrate how statistical methods are used to consider these inputs and allocate survey effort among different strata and instruments. We will also discuss statistical analyses that are used to look for unusual observations and evidence of material diversion after the data are collected. The final part of this talk will provide insights into working at a national lab and discuss opportunities for students at all levels.

Dr. Ladera Barbee, Long Beach City College

### Abstract

Although flipped class models have been around for many decades, instructors have previously avoided this teaching practice. Due to experiences with remote instruction and a new desire for change, flipped learning is experiencing increased interest. Following a 1-year sabbatical used to redesign my class, I implemented a fully Flipped Statistics course at Long Beach City College in 2015. Based on my experience, I will be share design components of a flipped class, how I execute my class, pros and cons for the model, lessons learned, and advice to flip your class.

With experience teaching at multiple community colleges both as an adjunct instructor and full-time professor, along with my current role as department Co-Chair, I will discuss a career in the Community College system. Additionally, I will provide advice for the full and part-time hiring process.

### Bio Sketch

Dr. Ladera Barbee is a Full-Time Professor and Co-Chair for the Department of Mathematics and Engineering at Long Beach City College. Additionally, she is the course coordinator for Business Calculus at California State University, Long Beach. She recently earned her Ed.D in Higher Education Leadership where her dissertation consisted of action research studying the application of collaborative learning skills to the students in her flipped statistics course.

## Spring 2022

Dr. Liz Vivas, Ohio State University

### Abstract

Given a polynomial f and a number x, we are interested on understanding (in general) the orbit of x under the action of f: that is the sequence of numbers: x, f(x), f(f(x)), etc. We will survey relevant results when we take x to be a complex number. I will also explain the challenges when we take more general maps and spaces.

### Bio Sketch

Dr. Vivas received her Ph.D. in mathematics from the University of Michigan under the direction of Prof. Berit Stensones. After graduating, she had postdoctoral positions at Purdue University at Lafayette, IN, Institute Henri Poincaré at Paris, and Universidad Federal Fluminense at Rio de Janeiro.

Hongyi Sheng, UC Irvine

### Abstract

Recent laureates of the Nobel Prize in Physics have inspired people to notice the beauty of black holes and general relativity once again. On Apr. 10, 2019, astronomers captured the first image of a black hole. This was a huge progress, for once we know the area of the event horizon, we actually get an estimate of the mass of the black hole. In fact, earlier in 1973, R. Penrose conjectured that given the dominant energy condition, the total mass of a space-time which contains black holes with event horizons of total area A should be at least (A/(16π))^{1/2}. An important special case in Riemannian geometry is now known as the Riemannian Penrose inequality. This inequality was first established by G. Huisken and T. Ilmanen in 1997 using the inverse mean curvature flow for a single black hole and then by H. Bray in 1999 for any number of black holes, using the technique of a conformal flow. Later in 2009, H. Bray and D. Lee generalized Bray’s result to dimension up to 7. In this talk, we will mainly focus on the construction of Bray's conformal flow in dimension 3. We will see that the area of the horizon is a constant along the flow, and that the mass is decreasing, using the well-known positive mass theorem. The convergence to the Schwarzschild metric finally gives us the inequality.

### Bio Sketch

Hongyi Sheng, Ph.D. student at UC Irvine, will earn his doctorate degree this May under the supervision of Richard Schoen. Then he will work as Stephen E. Warschawski Assistant Professor at UC San Diego. His main research interests are in general relativity and geometric analysis.

Kai-Wei Zhao, UC Irvine

### Abstract

Jang's equation arose from an embedding problem when P.S. Jang attempted to use Geroch's approach to prove positive mass conjecture in general relativity. This approach was not developed due to lack of existence and regularity of solutions to Jang's equation. In 1981, Schoen and Yau introduced a regularization procedure to construct a smooth solution to Jang's equation, and first gave a complete proof of the positive mass theorem using a different approach. In this talk, we will briefly introduce the background knowledge of general relativity and related topics, including initial data sets, marginally outer trapped surfaces and mass.

### Bio Sketch

Kai-Wei Zhao, Ph.D. student at UC Irvine, is going to get the doctor degree in math this May under the supervision of Richard Schoen. Then he will work at University of Notre Dame as Kenna Visiting Assistant Professor of Mathematics. His main research interests lie in geometric analysis, general relativity and geometric flow.

Dr. Vilma Mesa, University Of Michigan

### Abstract

Recent laureates of the Nobel Prize in Physics have inspired people to notice the beauty of black holes and general relativity once again. On Apr. 10, 2019, astronomers captured the first image of a black hole. This was a huge progress, for once we know the area of the event horizon, we actually get an estimate of the mass of the black hole. In fact, earlier in 1973, R. Penrose conjectured that given the dominant energy condition, the total mass of a space-time which contains black holes with event horizons of total area A should be at least (A/(16\pi))^{1/2}. An important special case in Riemannian geometry is now known as the Riemannian Penrose inequality. This inequality was first established by G. Huisken and T. Ilmanen in 1997 using the inverse mean curvature flow for a single black hole and then by H. Bray in 1999 for any number of black holes, using the technique of a conformal flow. Later in 2009, H. Bray and D. Lee generalized Bray’s result to dimension up to 7. In this talk, we will mainly focus on the construction of Bray’s conformal flow in dimension 3. We will see that the area of the horizon is a constant along the flow, and that the mass is decreasing, using the well-known positive mass theorem. The convergence to the Schwarzschild metric finally gives us the inequality.

### Bio Sketch

Dr. Vilma Mesa is professor of education and mathematics at the University of Michigan. She is also a Faculty Associate at the Center for the Study of Higher and Postsecondary Education. She investigates mathematics instruction and resource use in post-secondary settings, with an emphasis on community colleges. She has conducted several analyses of textbooks and evaluation projects on the impact of innovative mathematics teaching practices for students in science, technology, engineering, and mathematics. She collaborated in the development of an instrument to assess the quality of videos of math instruction in postsecondary settings. In her collaborative work, she is studying the use of free, open source, open access, and interactive textbooks for college mathematics courses and developing an instrument to assess the mathematical knowledge needed to teach college algebra at community colleges. She is Associate Editor of *Educational Studies in Mathematics*. She has published over 40 articles in mathematics education. Prior to her career in education, Mesa was a systems programmer for the ministry of finances in Colombia and for the district of Bogotá, and a computing systems advisor for a large construction and hospitality firm in Colombia. She has a B.S. in computer sciences and a B.S. in mathematics from the University of Los Andes in Bogotá, Colombia, and a master's and a Ph.D. in mathematics education from the University of Georgia.

Dr. Neha Murad, Calico Life Sciences

### Abstract

There are a multitude of pathological conditions that affect human health, yet we currently lack a predictive model for most diseases, and underlying mechanisms that are shared by multiple diseases are poorly understood. We leveraged baseline clinical biomarker data and long-term disease outcomes in UK Biobank to build prognostic multivariate survival models for over 200 most common diseases. We construct a similarity map between biomarker-disease hazard ratios and demonstrate broad patterns of shared similarity in biomarker profiles across the entire disease space. Further aggregation of risk profiles through density based clustering showed that biomarker-risk profiles can be partitioned into few distinct clusters with characteristic patterns representative of broad disease categories. To confirm these risk patterns we built disease co-occurrence networks in the UK Biobank and US HCUP hospitalization databases, and compared similarity in biomarker risk profiles to disease co-occurrence. We show that proximity in the biomarker-disease space is strongly related to the occurrence of disease comorbidity, suggesting biomarker profile patterns can be used for both predicting future outcomes as well as a sensitive mechanism for detecting under-diagnosed disease states.

### Bio Sketch

Dr. Neha Murad is an Applied Mathematician with a Ph.D. in Biomathematics and a minor in Statistics from North Carolina State University. She is a senior data scientist in the Translational Computing team at Calico Life Sciences, where she uses a combination of epidemiological, bioinformatics and QSP models and tools to understand the biology that controls aging and lifespan. Prior to Calico, Neha was a postdoc at GSK where she was part of the Pharmacokinetics (PK) team and used systems models in combination with machine learning approaches to build Physiologically Based Pharmacokinetic (PBPK) Models.

When not building math models, Neha loves to volunteer for events promoting mathematics in women and minorities. She is a AAAS IF/THEN Ambassador and is deeply involved in STEM outreach for middle and high school girls.

Dr. Kimberly Ayers, CSU San Marcos

### Abstract

Consider a continuous function f that maps a compact set to itself. By the Brouwer fixed-point theorem, such a function must have a fixed point: a point x_{0} such that f(x_{0}) = x_{0}. Since f has the same domain and range, we can consider compositions of f with itself: f^{2}(x), f^{3}(x), f^{4}(x), and so on. In this talk, we'll consider what happens to these iterates, and more specifically, what happens to particular points as we apply f to them over and over again. Sometimes, we'll see that this sequence converges to the fixed point; other times, it may move away from a fixed point. It may be sucked into an oscillator, or it may bounce all over the place. We will also examine how we can change the stability of systems to manipulate them to behave how we want - to make unstable fixed points stable again.

### Bio Sketch

Dr. Kimberly Ayers is an Assistant Professor in the Mathematics Department at California State University, San Marcos. She's previously held positions at Carroll College in Helena, Montana, and Pomona College, in Claremont, California. She received her Ph.D. from Iowa State University in 2015. Her research is in the areas of dynamical systems, chaos theory, and ergodic theory, with special interest in applications to biological systems. She is also passionate about promoting diversity and equity in the mathematical sciences. When she's not doing math, you can find her riding her bike or rock climbing.

Dr. Priya Prasad, University of Texas at San Antonio

### Abstract

The COVID-19 pandemic has had an enormous impact on instruction at institutes of higher education, but amid the myriad challenges, it has also provided instructors with opportunities. In this context, we were awarded an IUSE grant to encourage the use of evidence-based instructional practices in an introductory mathematics course; the instructors of this course, having moved all their lectures to pre-recorded videos, were thus open to trying new instructional strategies in class. In this talk, I will describe the features of the project that leveraged the opportunities presented by the move to virtual instruction. Additionally, I will discuss the preliminary results from interviews with participants, including some surprising consequences of the disruption caused by the COVId-19 pandemic. This project is supported by the National Science Foundation (#2116187).

### Bio Sketch

Dr. Priya V. Prasad is an Associate Professor of Mathematics at University of Texas at San Antonio. She got her Ph.D. in Mathematics (with an emphasis in Math Education) from the University of Arizona in 2014. She is primarily interested in investigating mathematical knowledge for teaching at multiple levels.

Dr. Lara Alcock, Loughborough University, UK

### Abstract

This talk will cover a series of research studies on mathematical reading and how we might improve it in undergraduates. The first study used eye-tracking to investigate and compare reading behaviours in undergraduates and mathematicians - I will present evidence that mathematical reading differs from ordinary reading in specific ways, and that students engage in key comprehension behaviours less than mathematicians. The second study investigated the effects of *self-explanation training* on students' reading behaviours. Using a combination of eye-tracking and experimental studies, we established that this training encouraged students to read in a manner more like that of professional mathematicians, and that this had positive effects on their mathematical proof comprehension.

### Bio Sketch

Lara Alcock is a Reader in Mathematics Education at Loughborough University. She collaborates with colleagues, Ph.D. students and project students to conduct research on mathematical thinking and learning, specializing in reasoning among undergraduate mathematics students and professional mathematicians. She has also written four research-informed books for undergraduates and popular mathematics readers: *How to Study as a Mathematics Major*, *How to Think about Analysis*, *Mathematics Rebooted*, and *How to Think about Abstract Algebra*.

Dr. Amelia Stone-Johnstone, CSU Fullerton

### Abstract

Research and state legislation have been the impetus for academic reform at postsecondary institutions nationwide. The corequisite model of academic support has been championed as an effective institutional structure for providing greater access to gateway mathematics and overall college degree/certificate completion at these institutions (e.g., Kashyap & Mathew, 2017; Logue et al., 2016; Richardson 2021). During this talk I will discuss the departmental change initiative at one institution towards adopting the corequisite model. Leveraging the four-frame model of organizational change (Bolman & Deal, 2008), as adopted for higher education (Reinholz & Apkarian, 2018), I will illustrate how an instructional team transformed College Algebra at a public four-year institution. Through the establishment of the core goals of course coordination, increased collaborative learning, and entwining metacognitive activities within the corequisite curriculum, the team of instructors developed a College Algebra corequisite course to better support their student population.

### Bio Sketch

Dr. Stone-Johnstone is an Assistant Professor in the Mathematics department at California State University, Fullerton. Her research focuses on developing and assessing academic support mechanisms that support student learning in gateway mathematics courses. In addition, her research area includes equity, teacher professional development, and institutional change.

Brittany L. Marshall, Rutgers University

### Abstract

As part of the larger COURAGE study, this presentation will discuss some of our findings which characterize forms of benevolence in calculus and precalculus instructors' perceptions of instructional practices and how they contrast with Black and Latinx students' perceptions of the same practices as potentially racialized and gendered. Instructors perceived themselves as lacking both agency and responsibility to reform calculus instruction in ways that supported student retention in the calculus sequence, which they largely attributed to not having enough time to teach required topics and concerns about high student enrollment in these courses.

### Bio Sketch

Brittany L. Marshall is a third-year Ph.D. in Education student in Mathematics Education. She is interested in middle/high school mathematics teaching and learning as well as math identity development, specifically among Black girls. Prior to Rutgers, Brittany taught middle school and high school math in Chicago for almost a decade and practiced architecture in both Chicago and DC. She holds a master's degree in architecture from North Carolina State University and a bachelor of architectural studies from University of Illinois at Urbana-Champaign.

Priyanga Ganesan, Texas A&M University

### Abstract

Quantum graphs are an operator space generalization of classical graphs that have appeared in different branches of mathematics including operator systems theory, non-commutative topology and quantum information theory. In this talk, I will review the different perspectives to quantum graphs and introduce a chromatic number for quantum graphs using a non-local game with quantum inputs and classical outputs. I will then show that many spectral lower bounds for chromatic numbers in the classical case (such as Hoffman's bound) also hold in the setting of quantum graphs. This is achieved using an algebraic formulation of quantum graph coloring and tools from linear algebra.

### Bio Sketch

Priyanga Ganesan is a fifth year doctoral student at Texas A&M University working with Dr. Michael Brannan. Her research explores the interaction between operator algebras and quantum information theory through the study of quantum graphs and non-local games. Before starting her Ph.D., she completed an integrated Bachelors-Masters degree in Mathematics at the National Institute of Science Education and Research in India. She is actively involved with several diversity programs in mathematics, and has also served as the President of the TAMU Association for Women in Mathematics graduate student chapter, board member of the worldwide Operator Algebras Mentor Network, and co-founded an I DP program for Math graduate students at Texas A&M.

## Fall 2021

Dr. Cristina Runnalls, Department of Mathematics and Statistics, Cal Poly Pomona.

### Abstract

Multicultural children's literature, defined as children's literature which highlights the lived histories of historically underrepresented groups, has a long complex history in education. Many educators believe that such classroom materials provide opportunities for students to engage in culturally relevant experiences and experience a greater sense of belonging in the classroom. Along a similar vein, the use of children's literature that focuses on mathematics also has its own history in classrooms. Mathematically focused children's books serve the purpose of helping children learn mathematics through story, offering a connection between math and literacy. But how do these two ideas intersect? This talk shares emergent research that focuses primarily on the mathematical and cultural noticing of elementary pre-service teachers when examining multicultural and mathematical children's literature. I will also share similar experiences from work with in-service teachers K-6 teachers, as well as how ideas from the research may extend throughout the mathematics curriculum.

### Bio Sketch

Dr. Cristina Runnalls is an Assistant Professor of Mathematics and Statistics at Cal Poly Pomona. Her research focuses broadly on addressing issues of access and opportunity for culturally and linguistically diverse students in mathematics, grounded within a framework that acknowledges the powerful social, cultural, and political influences in the classroom. Within this thread, she works extensively with both pre-service and in-service teachers to help support their math classrooms towards becoming a more socially just and rehumanizing space.

Dr. Maria De-Arteaga, Information, Risk and Operation Management Department, University of Texas at Austin.

### Abstract

Machine learning (ML) is increasingly being used to support decision-making in many high-stakes settings. However, there is currently a gap between the design and evaluation of ML algorithms and the functional role of these algorithms as tools for decision support. The first part of the talk will highlight the role of humans-in-the-loop, and the importance of evaluating decisions instead of predictions, through a study of the adoption of a risk assessment tool in child maltreatment hotline screenings. The second part of the talk will focus on the gap between the construct of interest and the proxy that the algorithm optimizes for. We propose influence functions based methodology to reduce this gap by extracting knowledge from experts' historical decisions. In the context of child maltreatment hotline screenings, we find that (1) there are high-risk cases whose risk is considered by the experts but not wholly captured in the target labels used to train a deployed model, and (2) the proposed approach improves recall for these cases.

### Bio Sketch

Dr. Maria De-Arteaga is an Assistant Professor at the Information, Risk and Operation Management (IROM) Department at the University of Texas at Austin, where she is also a core faculty member in the Machine Learning Laboratory. She received a joint PhD in Machine Learning and Public Policy from Carnegie Mellon University, a M.Sc. in Machine Learning from Carnegie Mellon University, and a B.Sc. in Mathematics from Universidad Nacional de Colombia. Her research on algorithmic fairness and human-AI complementarity aims to understand the opportunities and risks of using machine learning (ML) for decision support, and to develop human-centered ML that can improve expert decision-making. Her work has been featured by UN Women and Global Pulse, and has received best paper awards at NAACL'19 and Data for Policy'6, and research awards from Google and Microsoft Research.

Dr. Xiaodong Yan, Department of Mathematics, University of Connecticut.

### Abstract

Smectic liquid crystals are formed by elongated molecules that are aligned and arranged in fluid-like layers. They are remarkable examples of a geometrically frustrated, multi-layer, soft-matter system. Ground states of smectic liquid crystals are characterized by flat, equally spaced, parallel layers. Due to spontaneously broken translational and rotational symmetry, singularities form in regions where the smectic order breaks down. When defects are present, the layers must bend and the resulting curvature is, in general, incompatible with equal spacing between them. The subtle interplay between the geometry of the layers and equal spacing imposes theoretical complications, and understanding the layer structure of a smectic liquid crystal is a challenging task. Mathematically, this can be imposed as a singularly perturbed variational problem and the smectic state is described by the minimum configuration of the limiting energy as the penetration length parameter goes to zero. In this talk, I will discuss some recent progress on sharp lower bound and compactness for a nonlinear model of smectic A liquid crystals. This is based on joint work with Michael Novack.

### Bio Sketch

Dr. Xiaodong Yan is a math professor in the University of Connecticut. Her research area is nonlinear partial differential equations. She is mainly interested in regularity issues and pattern formations for nonlinear PDEs coming from continuum mechanics and materials science. Yan gets her Ph.D from University of Minnesota with the advising of Vladimir Sverak. Before joining UCONN, Yan worked as a postdoc in the Courant Institute of Mathematical Sciences and assistant professor in Michigan State University.

Dr. Adi Tcaciuc, Department of Mathematical and Statistical Sciences, MacEwan University.

### Abstract

The Invariant Subspace Problem is one of the most famous problem in Operator Theory, and is concerned with the search of non-trivial, closed, invariant subspaces for bounded operators acting on a separable Banach space. Considerable success has been achieved over the years both for the existence of such subspaces for many classes of operators, as well as for non-existence of invariant subspaces for particular examples of operators. However, for the most important case of a separable Hilbert space, the problem is still open.

A natural, related question deals with the existence of invariant subspaces for perturbations of bounded operators. These type of problems have been studied for a long time, mostly in the Hilbert space setting. In this talk I will give an overview of the Invariant Subspace Problem and present a new approach to the “perturbation” questions, in the more general setting of a separable Banach space. I will focus on the recent history, presenting several new results that were obtained along the way with this new approach, and examining their connection and relevance to the Invariant Subspace Problem.

### Bio Sketch

Dr. Adi Tcaciuc is a professor of mathematics and department chair at MacEwan University, in Edmonton, Canada. He completed his doctoral studies in 2005 at the University of Alberta, under the supervision of Dr. Nicole Tomczak-Jaegermann. His general research area is Functional Analysis, with an emphasis on Banach spaces and Operator Theory. In particular, he is interested in questions related to the Invariant Subspace Problem.

Maria (Masha) Gordina, Department of Mathematics, University of Connecticut.

### Abstract

We will start with fascinating history of the Brownian motion and its applications. Then we will discuss its more modern appearance in different areas of mathematics such as probability, partial differential equations and geometric analysis. At the end recent research using Brownian motion on curved spaces will be mentioned.

### Bio Sketch

Maria (Masha) Gordina is a professor of mathematics at the University of Connecticut. Her research is at the interface between stochastic analysis, differential geometry, and functional analysis, including the study of heat kernels on infinite-dimensional groups. Gordina completed her doctorate in 1998 from Cornell University under the supervision of Leonard Gross. Gordina was awarded a Humboldt Research fellowship in 2005 (with renewals), and the Ruth I. Michler Memorial Prize of the Association for Women in Mathematics in 2009. She was named a Simons Fellow (2016) in Mathematics and Physical Sciences.

Ruijia (RJ) Chen, Data Scientist, Google Inc.

### Abstract

In this open discussion, you will learn what a typical day of a data scientist/analyst would look like. RJ will discuss different kinds of skill sets one may gain in early stages of their career progression. She will also share some personal experience about how to work in an environment where a DS works intensively with cross-functional teams, including other quantitative and qualitative researchers, product managers, engineers, marketers, sales, finance, etc.

### Bio Sketch

RJ started her career in the People Analytics team at Walmart, and then joined Intuit in QBOA's marketing and sales analytics team. She has now been with Google for the past 3.5 years as a data scientist for Growth Lab and the Behavioral Economics team, both are central teams that serve across all Google product areas. Her current role mainly focuses on Ads Ease-of-Use, critical user journey, advertiser success and retention, Google Press Tracker and user trust, etc.

Dr. Xavier Ramos Olivé, Department of Mathematical Sciences, Worcester Polytechnic Institute

### Abstract

When a string vibrates, it produces different pitches depending on its length. This is how guitarists can play several notes using only one string, or how ancient Greeks where able to play melodies on zithers. But what happens when we have surfaces that vibrate, like when playing a digeridoo or a handpan? Do their shapes affect the pitch? We will discuss the role that Ricci curvature plays here and introduce some recent developments regarding integral curvature conditions and the eigenvalues of the Laplacian.

### Bio Sketch

Dr. Ramos Olive is currently completing his third year as a Postdoctoral Scholar at Worcester Polytechnic Institute. Being originally from Barcelona, where he studied Mathematics and Physics, he obtained his PhD from the University of California, Riverside in 2019, under the supervision of Prof. Qi S. Zhang. His research interests are in Geometric Analysis, Differential Geometry and Global Analysis on Manifolds. Particularly, he studies analytic properties of manifolds and metric measure spaces with integral curvature assumptions. He has published several eigenvalue estimates on manifolds under integral Ricci curvature assumptions, as well as estimates on the Neumann heat kernel on this kind of spaces.

Dr. Kate Melhuish, Texas State University

### Abstract

In recent years, professional organizations in the United States have suggested undergraduate mathematics shift away from pure lecture format. However, in the proof-based setting, transitioning to a student-centered class is a complex undertaking that involves managing a number of tensions related to staying authentic to student contributions while promoting the mathematical norms of the discipline. In this presentation, I'll discuss how high leverage teaching practices (HL TPs) (established in the K-12 literature) can be adapted to the proof context in order to help manage these tensions. In particular, I'll focus on a set of abstract algebra tasks that we have been developing as part of an NSF grant, Orchestrating Discussions Around Proof. We will spend some time engaging with the tasks and examining the ways that students approach them. I'll conclude with discussion and illustrations of various HL TPs and how they can support student engagement in the classroom.

### Bio Sketch

Dr. Melhuish is an Associate Professor of Mathematics at Texas State University. Their research focuses on the promotion of student-centered classrooms with attention to measures and instructional practices. Dr. Melhuish leads the design and development of the Group Theory Concept Assessment, the Math Habits Instructional Observation Tool (NSF #1814114), and is part of project teams developing proof comprehension tests in real analysis (NSF #1821553) and modelling self-efficacy assessments (NSF #1750813). Additionally, they have served as PI (NSF #1836559) and co-PI (NSF #122307 4) on grants studying interventions to promote more student-centered classrooms ranging from advanced mathematics to elementary level.

Dr. Henry Scharf, Department of Mathematics & Statistics, San Diego State University

### Abstract

The social structure of a population can often influence movement and inform researchers on a species' behavioral tendencies. Social networks can be studied through movement data; however, modern sources of data can have complex patterns of missingness that are not straightforward to address using existing methods. For example, drone-gathered observations of trajectories, while highly precise, can introduce labeling issues when individuals in a study population move in and out of the camera's active field of view. When individuals cannot be uniquely identified visually, multiple labels may be assigned to a single individual. Since all available social movement models rely on unique identification of all individuals in the population, we extend an existing Bayesian hierarchical movement model that makes use of a latent social network to accommodate "multiply-labeled" movement data. We apply our model to drone-gathered observations of dolphins to study the effect of sonar exposure on the dolphins’ social structure. Our proposed framework can be applied to all unlabeled movement data for various social movement applications and has potential implications for the study of privacy-protected movement data.

Dr. Estrella Johnson, Department of Mathematics, Virginia Tech (Estrella Johnson website)

### Abstract

Inquiry-oriented instruction has shown promise in regards to many features of student success, including conceptual understanding, affective gains, and persistence in STEM degrees. However, instructional change is difficult (especially at scale) and the research literature has documented a number of challenges instructors face when shifting their instructional practice. During this talk I will provide a characterization of inquiry-oriented instruction; discuss an instructional support model that was developed to support inquiry-oriented instruction in undergraduate mathematics courses; and present preliminary evaluation findings, drawing on a national sample of content assessment data, collected from 513 students at 46 different institutions. Analysis of this assessment data revealed no difference in the performance of men and women in the comparison sample; however, under the inquiry-oriented treatment, a gender performance difference was present - with men outperforming women. In an effort to understand this finding, I present related research literature on gendered experiences in collaborative settings and some of our ongoing analysis into the experiences of our students in these inquiry-oriented courses.

### Bio Sketch

Dr. Johnson is the Director for Inclusion and Diversity for the College of Science, and a Associate Professor of mathematics, at Virginia Tech. Her research focuses on the pedagogical practices of mathematicians, with the goal of better understanding and supporting high quality, ambitious teaching in undergraduate mathematics classrooms. She has worked extensively on investigating and supporting mathematicians as they work to implement inquiry-oriented instructional materials (NSF #143195). Additionally, Dr. Johnson has worked on large-scale national survey projects investigating instructional practice, and influences on practice, in undergraduate STEM education (e.g., NSF #1430540, NSF #0910240, NSF #1726281).

Dr. Xiaochuan Tian, Department of Mathematics, UC San Diego

### Abstract

Nonlocal continuum models are in general integro-differential equations in place of the conventional partial differential equations. While nonlocal models show their effectiveness in modeling a number of anomalous and singular processes in physics and material sciences, for example, the peridynamics model of fracture mechanics, they also come with increased difficulty in computation with nonlocality involved. In this talk, we will give a review of the asymptotically compatible schemes for nonlocal models with a parameter dependence. Such numerical schemes are robust under the change of the nonlocal length parameter and are suitable for multiscale simulations where nonlocal and local models are coupled. We will discuss finite difference, finite element and collocation methods for nonlocal models as well as the related open questions for each type of the numerical methods.

Dr. Katherine Kinnaird, Smith College. (Katherine Kinnaird website)

### Abstract

Data science seems to be everywhere these days. This talk will discuss examples of data science being applied to music and TED talks, as well as introducing publicly available resources for exploring culturally motivated data. This talk will delve deeply into the multidisciplinary field of Music Information Retrieval (MIR) motivated by the comparisons that we, as humans, make about music and the various contexts of these comparisons. By defining tasks such as building better song recommendation systems or finding structural information in a given recording, MIR seeks to algorithmically make these musical comparisons in the same manner that a human being would, but on a much larger scale. In this talk, we will introduce the field of MIR, including popular tasks and cutting edge techniques, including aligned hierarchies, a structure-based representation that can be used for comparing songs, and new extensions of aligned hierarchies that leverage ideas from topological data analysis.

Dr. Michael Barany, History of Science, University of Edinburgh (Michael Barany website)

### Abstract

If mathematics is in principle universal, mathematicians certainly are not. The striking demographic differences between the world of mathematicians and the world at large are a product of the history of where and how mathematicians have been trained, supported, and celebrated. In the twentieth century, a particular image of mathematics as a "young man's game" came to dominate both popular images of mathematicians and many mathematicians' own ideas of who can do mathematics and how. I will identify specific historical circumstances and developments that made mathematics appear to be a "young man's game" in the context of the politics and institutions of an internationalizing discipline. These circumstances converge in the quadrennial International Congresses of Mathematics and the history of the Fields Medal, which has become an accidental symbol of the preeminence of young men in modern mathematics. Recognizing the history, contingency, and politics of this dominant mathematical identity and image can offer a means of understanding and confronting present and future challenges around identity and diversity that continue to matter for mathematics and mathematicians.

## Spring 2021

Tao He (San Francisco State University)

### Abstract

T cells represent a crucial component of the adaptive immune system. Antigen-specific recognition is realized via T cell receptor (TCR), which is the product of somatic V(D)J gene recombination, plus some random addition/subtraction of nucleotides at recombination junctions. In this study, we aggregated the clones based on V/J gene segments, which overcomes the limitation and thus can build machine learning models across subjects. Here we presented a comparative study of different feature selection and classification on two multiclass Next-Generation Sequencing TCR repertoire data in cancer studies. We also proposed a novel ensemble of feature selection and demonstrated the method in simulation studies.

### About the Presenter

Tao He is an Assistant Professor of Statistics in the Department of Mathematics at San Francisco State University. She received her PhD in Statistics and dual PhD in Quantitative Biology from Michigan State University in 2015. Currently, she also serves as the President of San Francisco Bay Area Chapter of American Statistical Association. Dr. He’s research interests include statistical genetics/genomics, high-dimensional statistical inference, non- and semi-parametric models, statistical learning and their applications in biomedical research.

Aditya Adiredja (University of Arizona)

### Abstract

In this presentation I argue that engaging in anti-deficit work about students’ mathematical thinking is an accessible way to begin work on dismantling structural inequities in mathematics education. I will define what I mean by an anti-deficit perspective and its role within the equity project in mathematics education. I will share different projects from my program of research and how they embody the anti-deficit perspective. I will illustrate with findings from my work how such perspective has allowed me to challenge oppressive norms, and more importantly, to reimagine and construct different possibilities for students of color in mathematics and STEM more broadly.

### About the Presenter

Dr. Adi Adiredja is a teacher researcher whose work examines the role of race and gender in undergraduate mathematics education. His work continues to problematize how traditional cognitive work in mathematics education can engage with the politics of knowledge and learning, particularly pertaining to students of color.

Robin Wilson (California State Polytechnic University, Pomona)

### Abstract

Although, motivated by chemistry, spatial graph theory has now become a subfield of low dimensional topology closely related to knot theory. In particular, the study of topological symmetry groups of graphs embedded in S^{3} can be thought of as a generalization of the study of symmetries of knots and links. For a given embedding, we are interested in the automorphisms of the graph that are induced by a homeomorphism of the 3-sphere. This subgroup of the automorphism group of the graph is known as the topological symmetry group of that embedding. We will discuss recent results classifying which groups can occur as the topological symmetry group of some embedding of the Heawood graph in S^{3}.

### About the Presenter

Dr. Robin Wilson is a Professor of Mathematics at California State Polytechnic University, Pomona. He received his Ph.D. from UC Davis and joined the faculty at Cal Poly Pomona in 2006. In addition to maintaining an active research program in low-dimensional topology, Dr. Wilson also works in the field of mathematics education with a focus on equity and access of underserved youth which has come out of his involvement with the Algebra Project. He takes pride in the work that he has done throughout his time at Cal Poly Pomona and around Los Angeles. “I’ve been able to help young people, mostly from working-class backgrounds, learn not just about mathematics, but about what they themselves are capable of and pushing them to unlock their potential and prepare for a brighter future,” Wilson said. “I’m also proud of the community of mathematicians and educators that I am a part of that are fighting every day to re-humanize mathematics and re-imagine our place in it.” Dr. Wilson was The Network of Minorities in Mathematical Sciences’ 2018 Black History Month Honoree.

Prof. Ovidiu Munteanu (University of Connecticut)

### Abstract

An end of a manifold is an unbounded connected component of the topological space that results after removing some compact subset from the manifold. Finding the number of ends of noncompact manifolds is an important question. The talk will present some useful analytic techniques for counting the number of ends of manifolds. We will survey several classical results, and also present some more recent development.

### About the Presenter

Ovidiu Munteanu is an Associate Professor in the Department of Mathematics at the University of Connecticut. His research interests are in differential geometry and partial differential equations. Ovidiu gets his PhD in UC Irvine under the advising of Peter Li. He was Ritt Assistant Professor in Columbia University before joining UCONN. Besides of teaching and research, Ovidiu enjoys solving interesting math problems with undergraduate students and organizing math problem seminars and Putnam competitions.

Ying-fen Lin (Queen's University Belfast)

### Abstract

Let G be a locally compact group. It is known that the group C*-algebra can be defined by taking completion of L1(G) with respect to the C*-norm given by the irreducible unitary representations of G. However, if the group is not abelian, there is no concrete description of its group C*-algebra. In my talk, I will first introduce the C*-algebra of a group and then give a survey of results on certain classes of groups whose C*-algebras can be explicitly described.

### About the Presenter

Dr. Ying-Fen Lin is a Senior Lecturer in the School of Mathematics and Physics at Queen's University Belfast. She obtained her PhD in 2005 from National Sun Yat-Sen University. Her research interests are in the areas of Operator Algebras, Abstract Harmonic Analysis, Linear Preservers and their interactions. More specifically, she is interested in operator algebras arising from locally compact groups, and in their concrete descriptions in terms of operator fields, as well as their rigidity properties.

Naneh Apkarian (Arizona State University)

### Abstract

Undergraduate mathematics teaching and learning are cultural activities, situated within communities. Understanding aspects of these communities and their cultures can reveal much about how current practices work, and how we might change them for the better. This seminar will include: an overview of relevant theories; how to gather and interpret social network data related to education; and results from research studies.

Much of the talk will center on an investigation of instructional leadership at five university mathematics departments, in the context of lower-division mathematics courses. Guided by sociocultural theories, we use social network analysis to identify patterns of influence on instruction using the relations: seeking advice, sharing instructional materials, discussing instructional matters, and explicitly influencing teaching approach. Analysis of social network data gathered through surveys indicates that in these five communities, not all those with hierarchical authority have real influence over instructional practice, but those with the most influence over instruction do hold formally recognized positions.

Time permitting, preliminary results from ongoing work related to classroom participation patterns – and students’ perceptions of those patterns – will also be presented as an example of using social networks to investigate classroom-level phenomena.

### About the Presenter

Dr. Naneh Apkarian is an Assistant Professor of Mathematics Education in the School of Mathematical and Statistical Science at Arizona State University. She joined ASU in Fall 2020, amidst the COVID-19 pandemic. Dr. Apkarian's research involves many aspects of undergraduate mathematics education, primarily at a systemic or program level. She uses quantitative and qualitative research methods to better understand department and classroom level communities, students' experiences in mathematics courses, how students engage with mathematics content, and how to affect changes in STEM education. While Dr. Apkarian's work ranges across a variety of topics and contexts, it all contributes to a goal of creating a more inclusive and supportive STEM education system.

Dr. Ben Hayes (University of Virginia)

### Abstract

I'll discuss joint work with Keaton Hamm and Armenak Petrosyan. In it, we investigate a rearrangement problem for Fourier series introduced by P.L. Ulyanov, who conjectured that every continuous function on the circle admits a rearrangement of its Fourier coefficients such that the rearranged partial sums of the Fourier series converge uniformly to the function. We give several new equivalences to this conjecture in the context of operators on Hilbert spaces, and how these motivate weaker version of this rearrangement conjecture. Time permitting, I'll discuss how our work gives new characterizations of classical function spaces, as well as how this motivates problems for convolution operators on nonabelian groups. This talk will be accessible to a general audience.

### About the Speaker

Ben Hayes is an assistant professor at the University of Virginia. He obtained his PhD in 2014 at the University of California, Los Angeles, and was previously a postdoc at Vanderbilt University from 2014-2017. He received a postdoc research award from Vanderbilt University. His research interests are in von Neumann algebras, entropy of dynamical systems, free probability, soficity of groups, and measured group theory.

Dr. Mario Banuelos, (Fresno State)

### Abstract

Genomic anomalies, or variations, are often shared between members of the same species. Although rare, these changes may result in disease or an increase in host fitness. Most approaches for detecting structural variation rely on high quality data and are typically limited to one type of structural variant such as deletions or inversions. These genomic changes and interactions are often difficult to detect. Standard approaches for identifying such variation involves comparing fragments of DNA from the genome of interest to a reference genome. This process is usually complicated by errors produced in both the sequencing and mapping process which may result in an increase in false positive detections. In this work, we describe gradient boosting, neural network, and recommendation systems approaches in the context of genomic variants.

### About the Speaker

Mario Banuelos is an Assistant Professor of Mathematics at California State University, Fresno. He is from the small, agricultural town of Delano, California and a first-generation college student. Dr. Banuelos earned his B.A. in Mathematics from California State University, Fresno (Fresno State), and he obtained a Ph.D. in Applied Math from the University of California, Merced. His research interests include mathematical biology, optimization, statistical models for genome evolution, and data science. He is currently the program director for the SIAM Activity Group on Applied Mathematics Education.

Belin Tsinnajinnie (Santa Fe Community College)

### Abstract

Diversity and inclusion projects to support aspiring and current mathematicians from marginalized communities are often framed through some need for diversity and inclusion to advance the fields of mathematics. However, these conversations often fail to center the needs and goals of marginalized and underrepresented communities. In this talk, I discuss diversity and inclusion initiatives through a lens that is informed by frameworks that identify mathematics education as settler colonialism and my own experiences of inclusion/exclusion.

I call for a shift in the ways we can frame conversations of justice, equity, diversity, and inclusion in community college settings by asking: How do diversity and inclusion efforts in mathematics and mathematics education directly empower marginalized communities?

Nan Hu (Genentech Inc.)

### Abstract

This talk will give you a sneak peak of how applied mathematics and statistics are used in the biotech industry. I will first introduce an important statistical model in late-phase clinical trials: random coefficient regression model (RCRM). Through an examination of the RCRM, this talk then illustrates how mathematics can influence key decisions in a biotech company. I will also discuss the skillset needed for an industry job and how you can get ready for it as a graduate student. Lastly, a brief description of Genentech will be presented.

### About the Presenter

Nan Hu is currently a Principal Statistical Scientist at Genentech Inc. He obtained his Ph.D. in Applied Mathematical & Computational Sciences from the University of Iowa in 2016; he also holds a MS degree in Biostatistics from the University of Iowa.

Over the past ~5 years, Nan has served as the study statistician on multiple Phase I, II, and III Alzheimer’s clinical trials. Nan is currently the project lead statistician on crenezumab Alzheimer’s program, serving as a member of the Genentech global development team. In early 2019, Nan was a key member coming up with statistical strategies on crenezumab Phase III futility analysis. Nan is also a member of the cross-industry working group on endpoints in early Alzheimer’s disease.

In 2020, Nan also worked as the study statistician on a COVID-19 Phase III clinical trial at Genentech.

*Full title: "I Do Think Race and Gender Play a Role… I Would Analyze That Statement and Think, ‘Oh, Should I Not Take STEM?'”: Problematizing Neutrality in Undergraduate Calculus Instruction Entrenched in Racialized-Gendered Logics and Mechanisms of Inequality*

Dr. Luis Leyva (Vanderbilt University)

### Abstract

In this presentation, I characterize seemingly neutral features of undergraduate calculus instruction that insidiously contribute to the well-documented function of calculus in higher education as a racialized-gendered gatekeeper of advanced mathematics coursework and STEM majors. Drawing on published analyses of student interviews based on journaling of instructional events in calculus classrooms, I present how underrepresented students perceived seemingly neutral instructional practices as being entrenched in exclusionary logics that collide with stereotypes and other sociohistorical forces to fuel racialized-gendered mechanisms of inequality in student outcomes. In particular, my analyses revealed two logics in calculus instruction — (i) Instructors hold more mathematical authority than students; and (ii) Calculus is used to weed out students ’not cut out’ for STEM success — that underrepresented students perceived as producing inequitable opportunities for classroom participation, support from instructors and same-race/same-gender peers, and persistence in the calculus sequence and STEM majors. Throughout the presentation, I illustrate how ideologies of colorblindness and gender neutrality rooted in white supremacy and patriarchy, respectively, justify seemingly neutral instructional practices that have academically and socially damaging impacts on underrepresented students. I conclude the presentation by highlighting implications for practice in mathematics departments to support faculty with engaging in critical reflection and inquiry of their instructional practices, especially in introductory courses, that disrupt mechanisms of inequality rooted in white, patriarchal logics.

Dr. Hsioa-Fan Liu (Tamkang University, Taiwan)

### Abstract

The Sine-Gordon equation was discovered in the 19 century and S. S. Chern in 1981 gave a geometric interpretation of solutions to the Sine-Gordon equation, that is the pseudosphere. This relates partial differential equations and differential geometry. Such relation gives rise to the study of integrable systems and geometries. In this talk, we will recall the history of the Sine-Gordon equation and the pseudosphere at first. Then we will introduce some related and generalized questions with the known results. In the end, we will discuss our recent results on Heisenberg groups in this direction.

### About the Presenter

Hsiao-Fan Liu is an Assistant Professor of Mathematics at Tamkang University, Taiwan. Her research interests lie at differential geometry, PDE and discrete mathematics, especially integrable geometric curvature flows and integrable systems. She earned a PhD in mathematics from UC Irvine in 2014 (with Chuu-Lian Tern). Before joining Tamkang University, she has worked in Institute of Mathematics, Academia Sinica, Taipei and National Tsing Hua University as posdoc.

Dr. Chris Marx, Oberlin College

### Abstract

In this talk we will explore the dependence of the density of states for Schrödinger operators on the potential. The density of states characterizes the averaged spectral properties of a quantum system. Formally, it can be obtained as an infinite volume limit of the spectral density associated with finite-volume restrictions of a quantum system. Such limit is known to exist for certain quantum mechanical models, most importantly for Schrödinger operators with periodic and random potentials.

Following ideas by J. Bourgain and A. Klein, we will consider the density of states outer measure (DOSoM) which is well defined for all Schrödinger operators. We will explicitly quantify the parameter dependence of the DOSoM by proving a modulus of continuity with respect to the potential (in $L^\infinity$-norm and weak topology). This result is obtained for all discrete Schrödinger operators on infinite graphs and captures the geometry of the graph at infinity.

This talk is based on joint work with Peter Hislop (University of Kentucky).

### About the Presenter

Chris Marx is an Associate Professor of Mathematics at Oberlin College. His research interests lie at the intersection of analysis and mathematical physics, more specifically in spectral theory of Schrödinger operators. He earned a masters degree in theoretical and physical chemistry at the University of Vienna, Austria in 2007, and a PhD in mathematics from UC Irvine in 2012 (with S. Jitomirskaya). From 2012 to 2014, he held a postdoctoral position at Caltech as Harry Batement Instructor with Barry Simon. Since 2014 he has taught at Oberlin College, with promotion to Associate Professor in June 2020. In his spare time, Chris is a passionate amateur musician (harpsichord and voice), with a keen interest in early music and historical performance technique.

## Fall 2020

Dr. Carrie Diaz Eaton, Bates College

### Abstract

We are in a new age of digital information. Information is a form of power, and our students consume and produce more unfiltered information than ever. They need agency as individuals and tools as members of a future workforce to ethically and responsibly process this information. What is the role of mathematics instruction in helping students in their role as a digital citizen? I talk about my journey to developing an information literacy course using Open Educational Resources, including Calling Bull, Figure of the Day, and RStudio. This course serves as a forum to think meaningfully about probability, data analysis, and data visualization, a gentle introduction to programming, and a context to examine the interplay of information, power, and social justice. It also asks students to use these tools to explore and develop their own agency as a digital citizen.

### About the Presenter

Dr. Carrie Diaz Eaton's research in undergraduate interdisciplinary STEM education is grounded in community network theory and analysis. As an Associate professor of Digital and Computational Studies at Bates College in Maine, Dr. Diaz Eaton co-leads a number of digital community projects such as QUBES Director of Partnerships (Quantitative Undergraduate Biology Education and Synthesis) and Math Mamas. Carrie Diaz Eaton currently serves as the Chair for the Committee for Minority Participation in Mathematics for the Mathematical Association of America [MAA], is a MAA blogger for MathValues, and serves on the Editorial board of PRIMUS and CourseSource. She has also served as the past Program Chair and Electronic Communications Chair of BIO SIGMAA, as Education Subgroup Chair for the Society of Mathematical Biology, and for the editorial board for Letters in Biomathematics.

In 2012, Dr. Diaz Eaton was an MAA Project NExT Fellow, and in 2018 was selected as a Linton-Poodry SACNAS Leadership Institute Fellow. In 2020, Dr. Diaz Eaton was awarded the Society for Mathematical Biology John Jungck Excellence in Education Prize to recognize her for her work in interdisciplinary computational and mathematical biology education and mentorship. Dr. Diaz Eaton is also a proud 1st generation Latinx - her father is from Peru. She is also a mother. Dr. Diaz Eaton values the complex interplay at the intersection of her identities, professional activism in STEM education, and her research.

Kari Eifler, Texas A&M

### Abstract

Non-local games lie in the intersection of operator algebras and quantum information theory. In this talk, I will summarize some results of the operator algebraic approach to non-local games. I will especially focus on two examples: the graph isomorphism game and the metric isometry game, emphasizing the role of C*-algebras play in the study of these games. Finally, I will discuss how non-local games are able to shed light on the quantum symmetries of classical objects.

### About the Presenter

Kari Eifler is a PhD candidate at Texas A&M with plans to graduate in the summer of 2021. Her research lies within the areas of operator algebras and quantum information theory, with her dissertation focusing on quantum symmetries relating to non-local games. She previously completed her Masters of Mathematics at the University of Waterloo and her Bachelor of Science at the University of Alberta. During quarantine, she's enjoyed the opportunity to improve her cooking and baking skills.

Dr. Josh Hallam, Loyola Marymount University

### Abstract

The chromatic polynomial was originally defined by George Birkhoff as a tool to solve the famous four-color problem. Although it was not used in the eventual proof of the four-color problem, it has been shown to possess many interesting and unexpected properties. We will survey some of the properties and along the way see connections of the chromatic polynomial with other mathematical objects.

No background knowledge is required.

### About the Presenter

Josh Hallam obtained his PhD from Michigan State University in 2015. After that, he was a teacher-scholar postdoctoral fellow at Wake Forest University. He is currently an assistant professor at Loyola Marymount University. His research interests include enumerative and algebraic combinatorics.

Dr. F. Jay Breidt, Colorado State University

### Abstract

In this talk, I illustrate how many "small" but powerful statistical ideas (regression, interactions, likelihood ratios, multiple comparisons, mixtures, Monte Carlo, and more) can be combined to address a complex scientific problem. Experiments that longitudinally collect RNA sequencing (RNA-seq) data can reveal dynamic patterns of differential gene expression. Most existing tests are designed to distinguish among conditions based on overall differential patterns across time, but a variety of composite hypotheses may be of more scientific interest. Further, existing methods may lack power and some fail to control the false discovery rate (FDR). We propose a new model and testing procedure to address these issues simultaneously. Conditional on a latent Gaussian mixture with evolving means, we model the data by negative binomial regression, introduce a general testing framework based on the proposed model and show that the proposed test enjoys the optimality property of maximum average power. The test allows not only identification of traditional differentially-expressed genes but also testing of a variety of composite hypotheses of biological interest. We establish the identifiability of the proposed model, implement the proposed method via efficient algorithms, and demonstrate its good performance via simulation studies. The procedure reveals interesting biological insights when applied to data from an experiment that examines the effect of varying light environments on the fundamental physiology of a marine diatom.

This is joint work with Meng Cao, Novartis; Wen Zhou, Department of Statistics, Colorado State University; and Graham Peers, Department of Biology, Colorado State University

### About the Presenter

Jay Breidt, Professor of Statistics at Colorado State University, has research interests in survey sampling, time series, nonparametric regression, and uncertainty quantification for complex scientific models. He received his PhD at Colorado State University in 1991 and spent nine years at Iowa State University before returning to Colorado State in 2000. Breidt has been an associate editor for eight journals and reviews editor for Journal of the American Statistical Association and The American Statistician. He has served on six review committees for the National Academy of Sciences. He is past Chair of the American Statistical Association National Committee on Energy Statistics, has served two terms on the Federal Economic Statistics Advisory Committee, and is currently a member of the Census Scientific Advisory Committee. Breidt is an elected Fellow of the American Statistical Association and an elected Fellow of the Institute of Mathematical Statistics.

Dr. Aseel Farhat, Florida State University

### Abstract

We describe several aspects of an analytic/geometric framework for the three-dimensional Navier-Stokes regularity problem, which is directly inspired by the morphology of the regions of intense vorticity/velocity gradients observed in computational simulations of three-dimensional turbulence. Among these, we present our proof that the scaling gap in the 3D Navier-Stokes regularity problem can be reduced by an algebraic factor within an appropriate functional setting incorporating the intermittency of the spatial regions of high vorticity.

### About the Presenter

Aseel Farhat finished her PhD work in the Department of Mathematics at University of California Irvine in 2012. She was a Zorn Postdoctoral Fellow in the Department of Mathematics at Indiana University Bloomington between 08/2012 and 08/2015, and later joined the Department of Mathematics at University of Virginia as a Whyburn Instructor (Postdoc) till 08/2018. She is currently an Assistant Professor in the Mathematics Department at the Florida State University.

Aseel's main research area is fluid dynamics and analysis of non-linear PDEs. Her interests include well-posedness of geophysical models of ocean and atmosphere, continuous data assimilation (downscaling algorithms), feedback control, regularity criteria for the 3D Navier-Stokes equations, and geometry of turbulent flows.

Dr. Rui Wang, UC Berkeley

### Abstract

Symplectic geometry originated from classical mechanics. In this talk we first give a mathematical introduction to classical mechanics and quantum mechanics. Then we explain how the formalism of Symplectic Field Theory introduced by Eliashberg-Givental-Hofer, which is the most fruitful theory in symplectic geometry in the past 20 years, beautifully matches such theoretical mechanics framework. This talk is accessible to a general audience.

### About the Presenter

Rui Wang is working at UC, Berkeley. She got her Ph.D. degree in mathematics from University of Wisconsin-Madison. Her mathematical interests lie in symplectic geometry, contact geometry and mathematical physics. She enjoys research and teaching.

Dr. Jean Opsomer, Westat

### Abstract

Many important observational datasets in social sciences and public health are obtained through statistical surveys. A key strength of surveys is that the results of statistical analyses of survey data, properly performed, are statistically valid for inference about the overall population, without the need of additional assumptions. This is in contrast with non-survey observational data, whose representativeness needs to be justified on non-statistical grounds. However, analysis of survey data requires the use of specialized (weighted) approaches, which are not always available in standard statistical software. We will present an overview of the principles of survey design and estimation, and describe how survey-weighted analyses are performed and interpreted.

### About the Presenter

Jean Opsomer is Vice President at Westat, where he directs several large-scale survey and modeling projects for federal agencies and other clients. Previously, he spent 23 years as a faculty member in statistics, the majority of which at Iowa State University. His recent research has focused on the introduction of shape-constrained and nonparametric methods in survey estimation and on several interdisciplinary projects with survey components on a range of topics (higher education, public health, nutrition, employment, fisheries management, methane emissions, forest health, and agricultural erosion). The author or coauthor of 65 peer-reviewed articles, he has introduced a number of influential novel statistical methodologies into survey estimation. Dr. Opsomer is a Fellow of the American Statistical Association and the Institute of Mathematical Statistics, and an Elected Member of the International Statistical Institute.

Dr. Ian Duncan, UC Santa Barbara

### Abstract

Healthcare budgets in most countries seem to be out of control, with the U.S. heading to 20% of GDP and other countries not far behind in terms of rapidity of increases. Recently, predictive analytics, big data and artificial intelligence have been proposed as a solution that will enable practitioners to identify high risk populations and conditions earlier and intervene more effectively with patients. Is this hope justified or is it another example of mis-placed optimism? What will it take for predictive analytics to make a significant impact on the cost and value of healthcare? We propose that three factors are required to work together to effect transformation: Payment Reform; Predictive Analytics and Behavioral Economics. In the future, more outcomes risk will be transferred to providers and consumers of healthcare services. As risk professionals, actuaries will be a significant contributor to this transformation.

### About the Presenter

Ian Duncan is Adjunct Professor of Actuarial Statistics at the University of California Santa Barbara and president of Santa Barbara Actuaries Inc. a healthcare analytics firm. Dr. Duncan holds a graduate degree in Economics from Balliol College, Oxford and a PhD in actuarial statistics from Heriot-Watt University, Edinburgh. He is a fellow of a number of actuarial organizations. He is active in public policy and healthcare reform, and served on the board of directors of the Commonwealth of Massachusetts Health Insurance Connector Authority from 2007-2014 and the Society of Actuaries, 2012-5. He also serves on the advisory boards of several start-up healthcare companies. He is the author of more than 80 peer-reviewed papers, and several books and book chapters. His latest book, a second edition of "Healthcare Risk Adjustment and Predictive Modeling" (Actex Publications) was published in May 2018.

Dr. Yat Tin Chow, UC Riverside

### Abstract

In this talk, we explore image resolution and ill-posed-ness of inverse scattering problems. In particular, we would like to discuss how certain properties of the inclusion might induce high-resolution imaging. We first explore the super-resolution phenomenon with certain particular high contrast inclusion. We then discuss how local sensitivity (and resolution) around a point is related to the extrinsic curvature of the surface of inclusion around the point. Along the line, we also discuss concentration of plasmon resonance (in a certain manner) at boundary points of high curvature leveraging the Heisenberg picture of quantization and quantum ergodicity first derived by Shnirelman, Zelditch, Colin de Verdiere and Hellfer-Martinez-Robert. This is a joint work with Habib Ammari (ETH Zurich), Hungyu Liu (CityU of HK), Keji Liu (Shanghai Key Lab), Jun Zou (CUHK).

### About the Presenter

Yat Tin Chow is currently an Assistant Professor in the Department of Mathematics. He received his Ph.D. in Mathematics from the Chinese University of Hong Kong. He joined the faculty in UC Riverside after being a CAM assistant adjunct professor in Department of Mathematics in UCLA. His major research direction is applied mathematics. Dr. Chow's current research interests includes resolution analysis and enhancement of imaging from boundary measurements of various physical quantities, e.g. electric current, acoustic wave, light intensity, etc. He is also interested in computational methods of medical imaging and tomography, e.g. Electrical Impedance Tomography. Dr. Chow's other fields of interest include both theoretical and numerical aspects of large scale optimization method, computations of control methods and conflict modeling in high dimensional systems, as well as transportation plans and games between large populations in the mean field, and different phenomena that arise from this setting. If you are interested in his search areas, kindly visit Dr. Chow's personal website.

Dr. Junyuan Joanne Lin, Loyola Marymount University

### Abstract

This research aims to predict proteins' functions from protein-protein interaction (PPI) networks. The PPI networks we study include physical and genetic interactions between labeled and unlabeled proteins. This allows us to predict proteins' unknown functions based on the function labels of closely interacted "neighbors". In this presentation, I will present our award-winning graph-based algorithms that achieve the best prediction accuracy worldwide in the 2016 Disease Module Identification DREAM Data Mining Challenge. We define the diffusion state distance (DSD) metric, which sets appropriate distances to measure proteins' proximity on PPI networks as well as many other close-knit networks including social and energy networks. Fast algorithms, such as the unsmoothed aggregation algebraic multigrid method with random projections, are adopted to compute the DSD efficiently. Based on random walks combining with random projections, we propose graph-based methods to construct k-nearest-neighbor (kNN) graphs under the DSD metric for function prediction. We test our proposed algorithms on different networks to demonstrate that the computational cost of the algorithms is nearly optimal.

Prof. Janet Duncan, FCAS, FSA, MAAA

### Abstract

Insurance is a contractual promise to reimburse policyholders for future losses. Consumers often comment that they don't understand their insurance rates – it all seems very mysterious to them. But in reality, creating insurance rates is very logical when broken down into its component parts. The fundamentals of insurance ratemaking are very similar to the pricing of many other products, i.e., understanding cost and determining a target profit load. The major difference is that for many products, the cost is easily determined from the manufacturing process. However, for insurance, the cost involves significant uncertainty about the future. This presentation will introduce the audience to fundamental insurance principles and the mystery behind insurance ratemaking.

### About the Presenter

Professor Janet Duncan has over 30 years of property/casualty financial analysis experience, including commercial and personal lines reserving and pricing, financial and capital modeling, planning, and management reporting. Janet's work experience includes six years as CNA's senior vice president and signing actuary, responsible for $17 billion of property/casualty reserves, including standard commercial lines, specialty lines, and discontinued operations. Prior to CNA, Janet worked at XL Capital, serving in roles of increasing responsibility including executive vice president and chief finance officer of XL Insurance Europe and Asia. She also worked with PricewaterhouseCoopers LLP (consulting and audit support), and served in various actuarial roles with Aetna Life & Casualty where she began her insurance career. Janet has a bachelor's degree in Math/Actuarial Science from the University of Connecticut. She has served on many actuarial committees including the CAS Committee on Professionalism Education, the CAS Committee on Reserves, the AAA IFRS Task Force, the AAA Opinion Seminar Committee, and the SOA Strategic Planning Task Force. She is now working as a lecturer at the Department of Applied Probability and Statistics at UC, Santa Barbara.

Dr. Gülden Karakök, University of Northern Colorado

### Abstract

Numerous reports, policy and standards documents, and research studies emphasize the importance of creativity. For example, the recent report from the World Economic Forum noted that creativity at work is one of the top-three demanded skills, and that it "has jumped from 10th place to third place in just five years" (Schöning & Witcomb, 2017, para. 12). Within the domain of mathematics, similar emphases are made by mathematicians, mathematics education researchers and policy/standards makers. For example, the Mathematical Association of America's (MAA) CUPM Curriculum Guidelines (Schumacher & Siegel, 2015) for majors in the mathematical sciences states that "a successful major offers a program of courses to gradually and intentionally lead students from basic to advanced levels of critical and analytical thinking, while encouraging creativity and excitement about mathematics" (p. 9). In this talk, I will briefly summarize some of the research on mathematical creativity at the K-16 levels and introduce the work of the Creativity Research Group focusing on undergraduate mathematics courses. Our research group aims to explore ways in which undergraduate students' mathematical creativity can be fostered and explicitly valued in mathematics courses that include proof-construction and/or problem solving activities. I will introduce the Creativity-in-Progress Reflections (CPR) on Proving and Problem Solving tools that we designed. These formative assessment tools were created to enhance mathematical creativity (of users) while facilitating proof-construction and problem-solving heuristics as well as fostering metacognition. With two categories, Making Connections and Taking Risks, these formative assessment tools aim to develop mathematical discourse centered around aspects of creativity related to fluency, elaboration, flexibility, and originality. I will provide some examples of how one might implement these tools in various mathematics courses as well as discuss some illustrative empirical examples from our research studies.

## Spring 2020

*Note: Most of the Colloquia were cancelled due to COVID-19.*

Date | Title | Speaker and Affiliation |
---|---|---|

January 31, 2020 | Radar Topics with Quantitative Examples | Tim Rambach, Retiree from Raytheon |

## Fall 2019

Date | Title | Speaker and Affiliation |
---|---|---|

November 22, 2019 | Region Coverage from a Satellite ... (Insight into Industrial Mathematics) | Dr. Gary Green, retired from Aerospace Corporation |

November 19, 2019* | Learning turbulence from deep learning | Dr. Alessandro Corbetta, Eindhoven University of Technology |

November 15, 2019 | Bayesian Sparse Functional Principal Components Analysis Models Dynamic Temporal Changes in Longitudinal Microbiome Studies | Lingjing Jiang, UC San Diego |

November 8, 2019 | Applications of Mathematics in Telecommunications | Dr. Shabnam Sodagari, CSU Long Beach |

November 1, 2019 | Energy Stable Semi-Implicit Schemes for Allen-Cahn-Ohta-Kawasaki Model in Binary/Ternary System | Dr. Yanxiang Zhao, George Washington University |

October 25, 2019 | On the interplay of functional analysis and operator theory | Dr. Yunied Puig de Dios, UC Riverside |

October 11, 2019 | Property/Casualty Insurance Loss Reserving Methods | Janet Duncan, UC Santa Barbara |

October 4, 2019 | Impacts of Cellular Heterogeneity on Hair Follicle Growth Dynamics | Dr. Qixuan Wang, UC Riverside |

September 27, 2019 | Modeling Colony Pattern Formation under Differential Adhesion and Cell Proliferation | Dr. Jiajia Dong, Bucknell University |

## Summer 2019

Date | Title | Speaker and Affiliation |
---|---|---|

June 3, 2019 | Pseudocompact spaces -- Various Characterizations | Dr. Sudip Kumar Acharyya, University of Calcutta, India |

## Spring 2019

Date | Title | Speaker and Affiliation |
---|---|---|

May 3, 2019 | The Teichmüller TQFT | Dr. Jørgen Ellegaard Anderson, Aarhus University, Denmark |

April 19, 2019 | Chemical Reactions and Diffusions | Dr. Peyam Tabrizian, UC Irvine |

April 12, 2019 | Free-boundary Minimal Surfaces in the 3-ball with Connected Boundary | Dr. David Wiygul, CSU Long Beach |

March 8, 2019 | Expanding Competence: Uncovering the Possibilities of Children’s Mathematical Thinking | Dr. Nick Johnson, UCLA |

## Fall 2018

Date | Title | Speaker and Affiliation |
---|---|---|

October 19, 2018 | Mathematical Models of Human Immunodeficiency Virus Reservoirs | Dr. Naveen Vaidya, CSU San Diego |

October 12, 2018 | Fibonacci and Lucas Analogues of Binomial Coefficients and What They Count | Dr. Curtis Bennett, CSU Long Beach |

## Summer 2018

Date | Title | Speaker and Affiliation |
---|---|---|

June 14, 2018 | Characterizing pseudocompact spaces in terms of C-type intermediate rings | Sudip Kumar Acharyya, University of Calcutta, India |

June 8, 2018 | Abundance of nonisomorphic intermediate rings of continuous functions | Sudip Kumar Acharyya, University of Calcutta, India |

## Spring 2018

Date | Title | Speaker and Affiliation |
---|---|---|

April 27, 2018 | Study Gene Regulatory Networks Using Boolean Models | Dr. Yi-Ming Zou, University of Wisconsin-Milwaukee |

April 20, 2018 | New Ranking Measures and Algorithms for Expanding Robust Group Decision-Making Frameworks | Dr. Adolfo Escobedo, Arizona State University |

April 18, 2018 | Geometric Recursion | Dr. Jørgen Ellegaard Andersen, Aarhus University, Denmark |

April 13, 2018 | CNSM Munch N' Learn. Students Speak: What Professors Should Know | Students, CSU Long Beach |

April 6, 2018 | Finitely Additive Invariant Set Functions and Paradoxical Decompositions, or: How I Learned to Stop Worrying and Love the Axiom of Choice | Dr. Adam D. Richardson, CSU Long Beach |

March 16, 2018 | How to Predict the Fate of Schrodinger's Cat | Dr. Jim Stein, CSU Long Beach |

February 23, 2018 | Expansion Dynamics of Bacterial Populations | Dr. Jonas Cremer, UC San Diego |

February 16, 2018 | RNA secondary structures enumeration and prediction and their relation to moduli spaces | Dr. Jørgen Ellegaard Andersen, Aarhus University, Denmark |

February 9, 2018 | Interpolation of Manifold-Valued Functions | Dr. Evan Gawlik, UC San Diego |

February 2, 2018 | Discrete Means: generalizing a theorem of Kolmogorov and social choice | Dr. Curtis Bennet, CSU Long Beach |

## Fall 2017

Date | Title | Speaker and Affiliation |
---|---|---|

December 1, 2017 | Minimization of inhomogeneous biharmonic eigenvalue problems | Dr. Chiu-yen Kao, Claremont McKenna College |

November 3, 2017 | Distribution of Descents in Matchings | Dr. Gene Kim, USC |

October 27, 2017 | From Arrow's Social Choice Theorem to the compelling "dark matter" mystery | Dr. Donald Saari, UC Irvine |

October 20, 2017 | Shooting from singularity to singularity and a semilinear Laplace-Beltrami equation | Dr. Alfonso Castro, Harvey Mudd College |

October 6, 2017 | Mathematical Structures: Up Close and Afar | Dr. Stacy Musgrave, Cal Poly Pomona |

September 22, 2017 | From Macro to Micro and Back: Complexity, Simplicity and Optimality of Bacterial Cells | Dr. Matteo Mori, UC San Diego |

## Spring 2017

Date | Title | Speaker and Affiliation |
---|---|---|

June 8, 2017 | Relation between z-ideal and z^0-ideals in intermediate ring of continuous functions | Dr. Sudip Acharyya, University of Calcutta, India |

June 6, 2017 | Some new results on real valued continuous functions on a space X whose support lie on ideals of closed sets in X | Dr. Sudip Acharyya, University of Calcutta, India |

May 5, 2017 | Proof Comprehension at the Undergraduate Level: An Exploratory Study | Dr. Eyob Demeke, CSU Los Angeles |

April 14, 2017 | Spectra of compact composition operators on bounded symmetric domains | Dr. Dana Clahane, Fullerton College |

March 17, 2017 | Using Visual Art, Crafts and Music to Demonstrate Mathematics | Dr. Benjamin Dyhr, Metropolitan State University |

## Fall 2016

Date | Title | Speaker and Affiliation |
---|---|---|

December 2, 2016 | Non-Locality, Contextuality, and Topology | Dr. Kohei Kishida, University of Oxford |

November 18, 2016 | Outer Space and the Outer Automorphism Group of the Free Group | Dr. Catherine Pfaff, UC Santa Barbara |

November 10, 2016 | The Remarkable History of Exponents and Logarithms | Dr. Bob Stein, CSU San Benardino |

October 28, 2016 | Simulating Space: Role of Advanced Modeling and Uncertainty Quantification in JPL Missions | Dr. Lee Peterson, Jet Propulsion Laboratory |

October 21, 2016 | Data Science, Data Services, a Sabbatical Reflection | Dr. Khue Duong, CSU Long Beach |

October 11, 2016 | Lipschitz metric for a nonlinear wave equation | Dr. Geng Chen, University of Kansas |

September 23, 2016 | JPL Robotics | Dr. Gabriel Udomkesmalee, Jet Propulsion Laboratory |

September 2, 2016 | Nuclear Engineering for Everyone | Dr. Minh N. Tran, UC Davis |

## Spring 2016

Date | Title | Speaker and Affiliation |
---|---|---|

May 6, 2016 | Clots or not? Mathematics making the invisible visible | Dr. Ami Radunskaya, Pomona College |

April 29, 2016 | Generalized Wronskians and linear dependence of formal power series | Dr. Wai Yan Pong, CSU Dominguez Hills |

April 22, 2016 | A Relational Category of Formal Contexts | Dr. M. Andrew Moshier, Chapman University |

April 8, 2016 | Hearing the Shapes of Surfaces of Revolution | Dr. Thomas Murphy, CSU Fullerton |

March 4, 2016 | Liberal Arts Math | Dr. Jim Stein, CSU Long Beach |

February 19, 2016 | Geometry in the Dark Ages: Games of Shadows and Lights | Dr. Bogdan Suceava, CSU Fullerton |

## Fall 2015

Date | Title | Speaker and Affiliation |
---|---|---|

November 13, 2015 | Part I: Collaborative Filtering and the Yelp Dataset Part II: Python Introduction |
Students, CSU Long Beach |

October 30, 2015 | Two Applications of the Arithmetic of Elliptic Curves | Dr. Jasbir Chahal, Brigham Young University |

October 23, 2015 | Compact manifolds with integral bounds on the negative part of Ricci curvature and the Kato class | Dr. Christian Rose, Technische Universität Chemnitz |

October 16, 2015 | From Residuated Lattices to Boolean Algebras with Operators | Dr. Peter Jipsen, Chapman University |

October 9, 2015 | Energy driven pattern formation in thin fluid layers: The good, the bad and the beautiful | Dr. Andrew J. Bernoff, Harvey Mudd College |

September 11, 2015 | Numerical Simulation of Solvent Stokes Flow and Solute-Solvent Interface Dynamics | Dr. Hui Sun, UC San Diego |

## Spring 2015

Date | Title | Speaker and Affiliation |
---|---|---|

May 15, 2015 | Old and New Approximations for Bessel Functions | Dr. Mark Dunster, CSU San Diego |

April 24, 2015 | Alternating Volume, a Hyperbolic Invariant of Knots | Heidi Furlong and Leslie Rodriguez, CSU Long Beach |

April 17, 2015 | Analysis of 2+1 Diffusive-Dispersive PDE Arising in River Braiding | Dr. Charis Tsikkou, West Virginia University |

March 27, 2015 | Graph Representatives of Positroid Strata | Dr. Michaela (Puck) Rombach, UCLA |

March 13, 2015 | Can one hear the shape of a drum?---An Introduction to spectral theory in math physics | Dr. Shiwen Zhang, UC Irvine |

March 6, 2015 | Crimes with Undergraduates | Dr. Scott McCalla, Montana State University |

February 27, 2015 | Mathematica 10 & Wolfram Alpha Pro | Paul Fish, Wolfram Technologies in Education and Research |

February 20, 2015 | The Differential Geometry of the Maxwell Equations | Dr. Casey Kelleher, UC Irvine |

## Fall 2014

Date | Title | Speaker and Affiliation |
---|---|---|

December 5, 2014 | A Nonlinear Model for Tumor Growth: Global in time weak solutions | Dr. Konstantina Trivisa, University of Maryland |

November 14, 2014 | Dynamics of a soccer ball | Dr. Scott Crass, CSU Long Beach |

November 7, 2014 | Secure Computation and its Applications | Dr. Mehrdad Aliasgari, CSU Long Beach |

October 17, 2014 | How Wide is a 3-Manifold? | Dr. Diane Hoffoss, University of San Diego |

October 10, 2014 | Variational image segmentation with dynamic artifact detection and bias correction | Dr. Dominique Zosso, UCLA |

October 3, 2014 | Topic Point Processes | Dr. Blake Hunter, Claremont McKenna College |

September 26, 2014 | Knots, Fiber Surfaces, and the Building Blocks of Life | Dr. Matt Rathbun, CSU Fresno |

September 19, 2014 | Geotagging One Hundred Million Twitter Accounts with Total Variation Minimization | Dr. Ryan Compton, HRL Laboratories |

September 12, 2014 | An invitation to Floer homology | Dr. Ko Honda, UCLA |

## Spring 2014

Date | Title | Speaker and Affiliation |
---|---|---|

May 9, 2014 | Topological symmetry groups | Dr. Erica Flapan, Pomona College |

May 2, 2014 | Recent results on axially symmetric Navier-Stokes equations | Dr. Qi Zhang, UC Riverside |

April 17, 2014 | Geometric Methods for Graph Partitioning | Dr. Braxton Osting, UCLA |

February 28, 2014 | The Sound of Symmetry | Dr. Zhiqin Lu, UC Irvine |

## Fall 2013

Date | Title | Speaker and Affiliation |
---|---|---|

December 6, 2013 | Augmented Birack Homology | Dr. Sam Nelson, Claremont McKenna College |

November 15, 2013 | A Generalized Left-to-Right (GLR) parser for Tree-Adjoining Grammars (TAG) using Matrices | Nen Huynh, CSU Long Beach |

November 8, 2013 | Involutory Quandles of Knots | Dr. Jim Hoste, Pitzer College |

October 25, 2013 | Categorification and the Alexander polynomial | Dr. Kristen Hendricks, UCLA |

October 11, 2013 | From Soap Films to the Shape of Space | Dr. David Bachman, Pitzer College |

October 4, 2013 | An Illustrated Approach to Special Relativity and Its Paradoxes | Dr. John dePillis, UC Riverside |

September 27, 2013 | Adventures in Noether-Lefschetz Theory II: Base Loci, Singularities, and Class Groups both Geometric and Algebraic (Joint work with Scott Nollet at TCU) | Dr. John Brevik, CSU Long Beach |

September 20, 2013 | Kauffman Brackets on Surfaces | Dr. Francis Bonahon, USC |

September 6, 2013 | Adventures in Noether-Lefschetz Theory I: Curves, Surfaces, and Curves on Surfaces | Dr. John Brevik, CSU Long Beach |

## Spring 2013

Date | Title | Speaker and Affiliation |
---|---|---|

May 3, 2013 | A Brief Overview of Financial Mathematics | Dr. Triet Pham, USC |

April 19, 2013 | Using Forcing to Obtain a Model of the Continuum Hypothesis | Dr. Cynthia Northrup, UC Irvine |

April 12, 2013 | Cardiovascular Event Risk Dynamics Over Time in Older Patients on Dialysis: A Generalized Multiple-Index Varying Coefficient Model Approach? | Dr. Damla Senturk, UCLA |

March 22, 2013 | Mathematical Modeling of Language | Dr. Jacquelyn Rische, UC Irvine |

February 15, 2013 | Incidence Algebras | Dr. Muge Kanuni, Bogazici University, Istanbul, Turkey |

February 1, 2013 | Digital Microfluidics via Electrowetting | Dr. Ali Nadim, Claremont Graduate University |

January 25, 2013 | Exploring Ground States and Excited States of Spin-1 Bose-Einstein Condensates | Dr. I-Liang Chern, National Taiwan University |

## Fall 2012

Date | Title | Speaker and Affiliation |
---|---|---|

December 7, 2012 | Numerical Modeling of Transport Processes in the Subsurface | Dr. Antonella Sciortino, CSU Long Beach |

November 30, 2012 | Biomedical signal processing for the improvement of health care of patients with brain-related disorders | Dr. Shadnaz Asgari, CSU Long Beach |

November 16, 2012 | Machine learning, Balance cut and Total variation | Dr. Thomas Laurent, UC Riverside |

November 9, 2012 | Statistical Challenges in Molecular Diagnostics | Dr. Ming Ji, CSU San Diego |

October 19, 2012 | Fluids and Boundaries | Dr. James Kelliher, UC Riverside |

September 28, 2012 | A Little Big Problem in Graph Theory | Dr. Robert Mena, CSU Long Beach |

September 21, 2012 | Motion of Fluids in the Presence of a Boundary | Dr. Gung-Min Gie, UC Riverside |

## Spring 2012

Date | Title | Speaker and Affiliation |
---|---|---|

May 4, 2012 | Mathematics and Astronomy, Kepler's Laws of Planetary Motion | Dr. Arlo Caine, Cal Poly Pomona |

April 20, 2012 | Shape optimization problem involving principal eigenvalue in population dynamics | Dr. Chiu-Yen Kao, Claremont McKenna College |

April 13, 2012 | Helping Ford’s Fleet Customers Reach Their Sustainability Goals Through Optimization | Dr. Daniel Reich, Ford Motor Co. Research and Advanced Engineering |

February 24, 2012 | How to Distinguish a Football from a Basketball Mathematically | Dr. Jeremy Jankans, UC Irvine |

February 17, 2012 | Does a Statement of Whether Order Matters in Counting Problems Affect Students' Strategies? | Dr. Todd CadwalladerOlsker, CSU Fullerton |

January 27, 2012 | Stability theory of polytropic gaseous stars | Dr. Juhi Jang, UC Riverside |