DMS Colloquium: Haomin Zhou
Apr 19, 2024 04:00 PM
Please note special location for colloquium--Parker 228
Speaker: Haomin Zhou (Georgia Tech)
Title: Analysis and Computation of Parameterized Wasserstein Geometric Flow
Abstract: We introduce a new parameterization strategy that can be used to design algorithms simulating geometric flows on Wasserstein manifold, the probability density space equipped with optimal transport metric. The framework leverages the theory of optimal transport and the techniques like the push-forward operators and neural networks, leading to a system of ODEs for the parameters of neural networks. The resulting methods are mesh-less, basis-less, sample-based schemes that scale well to higher dimensional problems. The strategy works for Wasserstein gradient flows such as Fokker-Planck equation, and Wasserstein Hamiltonian flow like Schrodinger equation. Theoretical error bounds measured in Wasserstein metric is established.
This presentation is based on joint work with Yijie Jin (Math, GT), Shu Liu (UCLA), Has Wu (Wells Fargo), Xiaojing Ye (Georgia State), and Hongyuan Zha (CUHK-SZ).
DMS Colloquium: Dr. Grady Wright
Apr 12, 2024 04:00 PM
Refreshments will be served in Parker 244, 3:30-3:55pm.
Speaker: Dr. Grady Wright (Boise State University)
Title: A new framework for numerical integration
Abstract: Numerical integration, or quadrature, is ubiquitous in mathematics, statistics, science, and engineering, with a history dating back to the ancient Babylonians. A standard approach to generating quadrature formulas is to pick a "nice" vector space of functions for which the formulas are exact, such as algebraic or trigonometric polynomials. For integration over intervals, this approach gives rise to Newton-Cotes and Gaussian quadrature rules. However, for geometrically complex domains in higher dimensions, this exactness approach can be challenging, if not impossible since it requires being able to exactly integrate basis functions for the vector space over the domains (or some collection of subdomains). Another challenge with determining good quadrature formulas arises when the integrand is not given everywhere over the domain, but only as samples at predefined, possibly "scattered" points (i.e., a point cloud), which is common in applications involving experimental measurements or when quadrature is a secondary operation to some larger endeavor. In this talk we introduce a new framework for generating quadrature formulas that bypasses these challenges. The framework only relies on numerical approximations of certain Laplace operators and on linear algebra. We show how several classic univariate quadrature formulas can arise from this framework and demonstrate its applicability to generating accurate quadrature formulas for geometrically complex domains (including surfaces) discretized with point clouds.
Host: Ash Abebe
DMS Colloquium: Dr. Lateefah Id-Deen
Apr 05, 2024 04:00 PM
Speaker: Dr. Lateefah Id-Deen (Kennesaw State University, Georgia)
Title: Disrupting Injustice: Navigating Critical Moments in the Math Classroom
Host: Melinda Lanius
Bio:
Lateefah Id-Deen is an associate professor of mathematics education at Kennesaw State University and the founder of Loyal Educational Consulting. She works alongside teachers to incorporate culturally responsive pedagogical practices that promote student-teacher relationships, affirm mathematics identities, and cultivate belongingness to support students’ learning experiences in mathematics classrooms. Her work reflects her passion for creating equitable learning environments for historically marginalized students in mathematics classrooms. Connect with her on X @Prof_IdDeenL or LinkedIn/Facebook Lateefah Id-Deen
DMS Colloquium: Dr. Melinda Lanius
Mar 29, 2024 04:00 PM
Refreshments will be served in Parker 244, 3:30-3:55pm.
Speaker: Dr. Melinda Lanius (Auburn)
Title: Playing the villain: Approaches to validity in undergraduate mathematics education research
Abstract: In the setting of education research, a measure assigns a numerical value to represent the degree to which a target attribute appears; For example, a psychometric scale for math anxiety assigns a numerical value to indicate if an undergraduate student has high, medium, or low/no math anxiety. How do we know if a measure means what we think it means? We can collect evidence of validity! In this highly interactive talk, I will share my journey in understanding validity and the types of evidence we can use to assess the soundness of our measures. This reflective work has required me to look at my study designs unenthusiastically and critically, "playing the villain" in my own research program. Please come join me for an afternoon of fun, where we put on our critic hats and explore validity in undergraduate mathematics education research!
DMS Colloquium: Dr. Joseph Briggs
Mar 01, 2024 04:00 PM
Speaker: Joseph Briggs (Auburn University)
Title: A random walk through extremal combinatorics
Abstract: Extremal combinatorics broadly covers any kind of optimization where the structures you study are too discrete for smooth arguments to apply directly. So, it covers questions of the form: how large can a parameter be over a restricted class of sets or hypergraphs? I’ll introduce some problems of this kind and talk about a mixture of different results of mine from the last two and a half years.
DMS Colloquium: Peter McGrath
Dec 01, 2023 04:00 PM
Refreshments 3:30 p.m., Parker 244
Speaker: Peter McGrath (North Carolina State University)
Title: Calculus of Variations and the Bending Energy of Surfaces
Abstract: Beginning with the solution of the classical Plateau problem—the problem of finding an area-minimizing disk whose boundary is a prescribed simple closed curve in Euclidean 3-space—we will survey some applications of Calculus of Variations to solve geometric extremal problems. Particular emphasis will be placed on the problem of finding a smooth surface in 3-space with minimum total squared mean curvature and prescribed isoperimetric ratio and genus. Such minimizers of the total squared mean curvature (also called the bending energy) were proposed in 1970 by Biologist Peter Canham to model the shape of red blood cells and lipid bilayers.
