Mathematics Colloquium

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.