Mathematics Colloquium

Dr. Bogdan Suceavă, CSU Fullerton

Abstract

In 1827, C.F. Gauss obtained a relation that he described as "remarkable;" the fact that the curvature of a surface depends only on the elements of the first fundamental form. More than a century later, J. F. Nash's Theorem proved that any Riemannian manifold can be embedded into a Euclidean ambient space with dimension sufficiently large. In 1968, S.-S. Chern pointed out that a key technicality in applying Nash's Theorem effectively is finding useful relationships between intrinsic and extrinsic elements which characterize immersions. After 1993, when a groundbreaking work written by B.-Y. Chen on this theme was published, many explorations pursued the investigations of geometric inequalities between intrinsic and extrinsic quantities. With all these developments in mind, we propose a classification of geometric inequalities in the geometry of submanifolds in five classes; some of these relations might be well-known, while others are rather new.

Biosketch

Bogdan Suceavă studied mathematics at the University of Bucharest (B.Sc. 1994, M.Sc. 1995) and at Michigan State University (Ph.D., 2002). Since 2002, he has worked at Cal State Fullerton, where he wrote most of his over 80 papers in mathematics. He is one of the recipients of a 2020 MAA Polya Award for Expository Writing (for a paper written with A. Glesser, M. Rathbun, and I.M. Serrano). In the fall of 2011, Suceavă established the Fullerton Math Circle, an outreach program of our CSUF Math Department, focused on developing problem-solving skills in mathematics for K-12 students. Suceavă is the recipient of the Cal State Fullerton 2023 L. Donald Shields Excellence in Scholarship and Creativity Award, and an honorary research professor with the Babeş-Bolyai University in Cluj-Napoca, Romania.

Dr. Puttipong Pongtanapaisan, Arizona State University

Abstract

We learn in calculus that critical points provide key insights into the shape of a graph. In nature, various biological structures, such as systems of worms or water rings, often form naturally tangled configurations. In this talk, I will discuss how rearranging critical points can lead to conclusions about knotted shapes. For instance, if the order of certain local maxima and minima cannot be swapped, it indicates that the polymer cannot fit into a tight tube.

Biosketch

Puttipong Pongtanapaisan obtained his Ph.D. at the University of Iowa, where he studied knot theory and low-dimensional topology under the supervision of Dr. Maggy Tomova. He was a PIMS Postdoctoral Fellow at the University of Saskatchewan, working with Dr. Chris Soteros to explore knotted objects in lattice tubes by analyzing the arrangement of local maxima and minima of knots and links. Currently, he is a Postdoctoral Associate at Arizona State University.

Dr. Knut Solna, UC Irvine

Abstract

Many problems are characterized by uncertainty and best modeled using a probabilistic framework. In this talk I will describe aspects of my research relating to mathematical finance where uncertainty plays an important role. I will moreover describe the UCI mathematics program and aspects of applying to a graduate program.

Biosketch

Knut Solna is a Professor and Vice Chair for Graduate Studies in the Department of Mathematics at UC Irvine. He received his Ph.D. in 1997 from Stanford University, under the supervision of George C. Papanicolaou.

Dr. Solna's research interests span applied mathematics, applied probability, stochastic differential equations, mathematical finance, and waves in random media. He has received numerous accolades, including the Sloan Fellowship, an instructorship award from the University of Utah, a Fulbright Award, and research grants from the Air Force Office of Scientific Research and the National Science Foundation.

In addition to authoring over 100 high-impact research publications, Dr. Solna has written and edited five books on topics such as econometrics, risk management, and mathematical and statistical models for imaging, among others.

Alexandro Ricardo Luna, UC Irvine

Abstract

We discuss a survey of results concerning the dimensions of the spectra of Sturmian Hamiltonians and give an overview of the dynamical techniques that are used in small coupling regimes. We also present a new result concerning the behavior of the Hausdroff dimension of such a spectrum when the coupling tends to zero and the frequency is of bounded-type.

Biosketch

Alexandro Ricardo Luna is a 5th year graduate student at University of California, Irvine. Their research interests include spectral theory and dynamical systems. They attended California State University, Fullerton as an undergraduate and have been local to California their whole life.

Dr. Jamie Haddock, Harvey Mudd College

Abstract

The Kaczmarz methods are a family of simple, deterministic or randomized, iterative methods which can be employed for solving consistent systems of linear equations of the form Ax = b, or related problems. These methods have gained popularity in recent times due to their amenability to large-scale data and distributed computing environments. This talk will focus on results in three areas, all related in some way to the Kaczmarz methods: iterative methods for adversarially corrupted systems of linear equations; analyzing the dynamics of simple models of consensus amongst interacting agents; and proving bounds on the concentration and variance of randomized iterative methods.

Biosketch

Jamie Haddock received her B.S. in Mathematics from Gonzaga University, and Ph.D. in Applied Mathematics from University of California, Davis. After completing her degrees, Jamie joined UCLA for a three-year postdoctoral fellowship where she was mentored by Prof. Deanna Needell. She arrived at Harvey Mudd College in 2021 and is currently the Iris and Howard Critchell Assistant Professor of Mathematics.

Jamie leverages mathematical tools, such as those from probability, combinatorics, and convex geometry, on problems in data science and optimization, and has been active recently in topics like randomized numerical linear algebra, combinatorial methods for convex optimization, and tensor decomposition for topic modeling. She is especially interested in questions about complex and messy data, like that encountered in medical applications.

Dr. Amber Simpson, Binghamton University

Abstract

Informal learning environments offer opportunities to engage learners in authentic and humanistic ways to explore mathematical concepts and thinking. In this talk, I will provide examples to illustrate children's engagement with mathematical concepts in the following settings: (a) home environments through engineering design tasks; (b) an afterschool program focused on the integration of Western STEM concepts, practices, and processes with both archaeological and Indigenous concepts, practices, and processes; and (c) a school-based making space where learners programmed an educational robot.

Biosketch

Dr. Simpson's research focuses on increasing the participation of individuals from socially excluded groups in STEM career pathways, including technicians, middle-skills workers, and those pursuing advanced degrees. She also supports her research through STEM activities and events for children and their families in the community.

Dr. Po-Ning Chen, UC Riverside

Abstract

In this talk, we investigate the relation between the local property of a space (curvature) and its global properties. In particular, we will see that the existence of a metric with positive curvature restricts the topology and minimal submanifolds. We will also discuss the role of these objects in general relativity.

Biosketch

Po-Ning Chen is a mathematician working in geometric analysis. In particular, he uses partial differential equations to study problems in general relativity, such as the definition of mass in general relativity and gravitational waves. Dr. Chen is an associate professor at the University of California, Riverside. Dr. Chen earned a doctorate in mathematics from Harvard University in 2011 under the supervision of Shing-Tung Yau. Before joining UC Riverside, Dr. Chen worked as the Ritt Assistant Professor at Columbia University.

Dr. Jonathan Bostic, Bowling Green State University

Abstract

Validity and validation work has seen a recent surge in scholarship over the last decade, which has the potential to promote better measurement practices as well as improvements in understanding what students and teachers know. Our first objective in this talk is to briefly explore validity and validation through the Standards for Educational & Psychological Testing (AERA et al., 2014). Our second objective is to engage with a recently released assessment repository. Attendees will receive training about the contents of the repository and learn how to use it effectively.

Biosketch

Dr. Jonathan Bostic's primary area of scholarship focuses on exploring validity issues and trends in the context of measurement in mathematics education. He also investigates ways to enhance instructional contexts to better support teaching and learning, particularly learners' mathematical proficiency. His research agenda includes scholarship on mathematics tasks, learning environments, and teachers as they influence students' outcomes (e.g., problem-solving performance, contextualization of problem-solving, etc.).

Dr. Changho Kim, UC Merced

Abstract

The statistics-informed neural network (SINN) has been proposed as a machine learning-based stochastic trajectory generator [J. Comput. Phys. 474, 111819 (2023)]. With the capability of learning stochastic dynamics from time trajectory data and reproducing stochastic time trajectories faithfully and efficiently, this methodology is considered a promising tool for surrogate modeling. In this presentation, I’ll first introduce SINN and describe its unique structure and training scheme. Then, I’ll talk about extending SINN to multi-dimensions. Finally, I’ll discuss how SINN can be used for surrogate modeling in multi-scale multi-physics simulations.

Biosketch

Changho Kim's current research centers around stochastic modeling of multi-physics phenomena arising in fluids and soft matter at small scales. He develops and analyzes stochastic multiscale simulation methodologies and studies mathematical and physical foundations of stochastic mesoscopic modeling. The overall approach is based on the synergistic use of stochastic processes, computational fluid dynamics (CFD), molecular dynamics (MD), kinetic Monte Carlo (KMC), and statistical mechanics. The long-term goal of his research is to establish a unifying computational framework that facilitates our understanding of complex natural phenomena with multiple time and length scales, and bridges the gaps at the physics-chemistry-biology interface He received his Ph.D. in Applied Mathematics from Brown University (advisor: George Em Karniadakis). He also holds a Ph.D. in Chemistry from KAIST (Korea Advanced Institute of Science and Technology). Before joining UC Merced, he was a postdoctoral researcher at the Lawrence Berkeley National Laboratory (advisor: John B. Bell).

Dr. Robin Wilson, Loyola Marymount University

Abstract

Microaggressions are intentional or unintentional actions that communicate hostile, derogatory, or negative messages towards a recipient. Microaggressions that students receive in a math class can impact a students' learning experience and sense of belonging. We will discuss our analysis of the reflections of 184 undergraduate math students who were asked to reflect on an article about Mathematical Microaggressions. Findings show that a majority of the students in our study reported experiences that made them feel like they do not belong in the math classroom, and that racial, gendered, and mathematical microaggressions contribute to this. We will also share some ideas for affirming students' sense of belonging in the math classroom through microaffirmations. This research supports the need to develop initiatives at departmental and institutional levels to encourage more inclusive spaces in math and STEM classrooms.

Biosketch

 Dr. Robin Wilson earned his PhD in the Department of Mathematics at the University of California, Davis. He is currently a Professor in the Department of Mathematics at Loyola Marymount University. Prior to joining the faculty at LMU Dr. Wilson served as faculty in the Department of Mathematics and Statistics at California State Polytechnic University, Pomona for 15 years. Dr. Wilson has also been a Visiting Professor at Georgetown University and Pomona College. His scholarship includes both low-dimensional topology and the scholarship of teaching and learning. Dr. Wilson's work in mathematics education focuses on issues of equity and access for students of color in the K-12 and undergraduate mathematics classroom.

Dr. Konrad Aguilar, Pomona College

Abstract

(This is joint work with Karina Behera, Tron Omland, and Nicole Wu.) In this talk, I will discuss a first result in a new area that I've started to explore called quantum information theory as well as my journey into this field. My main area of research is quantum metric spaces, which was originally developed by Marc Rieffel to address some statements in the particle physics literature and is one of many fields of mathematics that mix concepts from calculus and linear algebra. Quantum metrics provide a notion of distance between quantum states, and therefore, a notion of distance between elements of an object in quantum information theory known as the density space. However, there already exist well-known metrics that provide distances between elements of a density space such as the Bures metric. Our work establishes comparisons of these metrics in a topological and metric sense. This work is partially supported by NSF grant DMS-2316892 and appears in the article https://arxiv.org/abs/2406.07219.

Biosketch

Konrad Aguilar is an Assistant Professor of Mathematics at Pomona College. Born and raised in Los Angeles County, he is a product of the California Community Colleges and the California State University systems. Aguilar does research in analysis, and in particular, C*-algebras and quantum metric spaces. He was recently awarded an NSF LEAPS-MPS grant, which focuses not only on advancing these areas, but also providing research opportunities for undergraduates and high school students from underrepresented groups in part through the Pomona College Academy for Youth Success (PAYS) program. He is also an active member of SACNAS and co-advises the Claremont Colleges SACNAS group.