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Differential Equations and Nonlinear Analysis Seminar: Hakima Bessaih, FIU, Various numerical scheme for stochastic hydrodynamic models
ZoomWe will consider various models in hydrodynamic, including the 2d Navier-Stokes, Boussinesq equations, and a Brinkman-Forchheimer-Navier-Stokes equations in 3d. These models are driven by an external stochastic Brownian perturbation. We will implement space-time numerical schemes and prove their convergence. We will show some rates of convergence as well. Furthermore, we will show the difference between…
Teaching and Learning Seminar: Molly Fenn and Patty Clemons, NC State, Desmos Activity Builder
SAS 4201Desmos Activity Builder is an online tool that can be used in a variety of ways in and out of the classroom. It can be used to introduce concepts or as a learning assessment during or outside of class. In this session we will explore some ways to use Desmos activities in your classroom. We…
Geometry and Topology Seminar: Peter J. Olver, University of Minnesota, Structure and Generators of Differential Invariant Algebras
SAS 1216The structure of algebras of differential invariants, particularly their generators, is based on the symbolic invariant calculus provided by the method of equivariant moving frames. I will discuss a new computational algorithm that will, in many cases, determine whether a given set of differential invariants is generating. As an example, we establish a new result…
Applied Math Graduate Student Seminar: John Darges, NC State, Sensitivity Analysis in Forward and Inverse Problems
SAS 4201Global sensitivity analysis (GSA) offers a flexible framework for understanding the structural importance of uncertain parameters in mathematical models. This dissertation focuses on forward and inverse problems arising in uncertainty quantification and the computation of Sobol’ indices, measures of variance-based sensitivity. The models involved in these prob- lems are often computationally expensive to evaluate. Sensitivity…
Biomathematics Seminar: Elizabeth Brunk, UNC, Elucidating Mechanisms of Uneven DNA Segregation and its Impact on Cellular Processes
Cox 306This talk will be in person in Cox 306 where snacks and refreshments will be provided, there will also be a virtual option for those who cannot attend in person. Speaker's website Zoom Link
Geometry and Topology Seminar: Adam Lowrance, Vassar College, The average value of invariants of 2-bridge knots.
ZoomWe show how to use continued fraction representations of 2-bridge knots to compute the average value of different invariants of the set of 2-bridge knots with fixed crossing number c. Examples include the Seifert genus, braid index, and the absolute value of the signature. We also mention other properties of the probability distributions of these…
Algebra and Combinatorics Seminar: Lorenzo Vecchi, KTH, Categorical valuative invariants of matroids
SAS 4201In this talk we define a new category of matroids, by working on matroid polytopes and rank preserving weak maps. This lets us introduce the concept of categorical valuativity for functors, which can be seen as a categorification of the ordinary valuativity on matroid polytope decompositions. We also show that this new theory agrees with…
Math Department Weekly Tea
SAS 4104Differential Equations and Nonlinear Analysis Seminar: Edouard Pauwels, Université de Toulouse, Nonsmooth differentiation of parametric fixed points
ZoomRecent developments in the practice of numerical programming require optimization problems not only to be solved numerically, but also to be differentiated. This allows to integrate the computational operation of evaluating a solution in larger models, which are themselves trained or optimized using gradient methods. Most well known applications include bilevel optimization and implicit input-output…
Algebra and Combinatorics Seminar: Emily McGovern, NC State, Thesis Defense
SAS 1216Speaker's website
Computational and Applied Mathematics – Differential Equations and Nonlinear Analysis Seminar: Alexey Miroshnikov, Discover Financial Services, Stability theory of game-theoretic group feature explanations for machine learning models.
SAS 4201In this article, we study feature attributions of Machine Learning (ML) models originating from linear game values and coalitional values defined as operators on appropriate functional spaces. The main focus is on random games based on the conditional and marginal expectations. The first part of our work formulates a stability theory for these explanation operators…
Stochastics Seminar: Amarjit Budhiraja, UNC-Chapel Hill, Large deviations for weakly interacting diffusions and mean field stochastic control problems
SAS 4201Consider a collection of particles whose state evolution is described through a system of interacting diffusions in which each particle is driven by an independent individual source of noise and also by a small amount of noise that is common to all particles. The interaction between the particles is due to the common noise and…
Teaching and Learning Seminar: Emily Braley (Johns Hopkins University) and Jack Bookman (Duke University), A survey of Programs Preparing Graduate Students to Teach Undergraduate Mathematics
ZoomPrograms Preparing Graduate Students to Teach Undergraduate Mathematics Zoom link
Biomathematics Seminar: Mikio Aoi, UCSD, TBA
Cox 306Zoom Link
Geometry and Topology Seminar: Thomas Wears, Longwood University, The Ricci Flow on Three-Dimensional Metric Lie Algebras
SAS 4201A metric Lie algebra is a real Lie Algebra with an inner product. In this talk, we will outline a complete classification of all three-dimensional metric Lie algebras up to notions of equivalence determined by isomorphism and scaling and investigate the Ricci flow on the resulting parameter spaces of equivalence classes.
Algebra and Combinatorics Seminar: Maximilian Kaipel, University of Cologne, Partitioned fans, hyperplane arrangements and K(pi,1) spaces
SAS 4201Polyhedral fans are geometric objects, which arise naturally in many areas of mathematics, for example in toric geometry, the theory of hyperplane arrangements and representation theory. In many cases, there are natural ways of identifying some of the polyhedral cones defining a fan, thus giving a "partition of the fan". To each such partitioned fan…
Differential Equations and Nonlinear Analysis Seminar: Wojciech Ozanski, FSU, Logarithmic spiral vortex sheets
ZoomWe will discuss a special family of 2D incompressible inviscid fluid flows in the form of logarithmic spiral vortex sheets. Such flows are determined by a vorticity distribution of a curve R^2, and they are notoriously hard to study analytically. In the talk we will discuss several results regarding logarithmic spiral vortex sheets: well-posedness of the spirals as…
Colloquium: Gadi Fibich, Tel Avis University, Effects of Network Structure on Spreading of Innovations
SAS 4201Spreading (diffusion) of new products is a classical problem. Traditionally, it has been analyzed using the compartmental Bass model, which implicitly assumes that all individuals are homogeneous and connected to each other. To relax these assumptions, research has gradually shifted to the more fundamental Bass model on networks, which is a particle model for the…
Financial Mathematics Seminar: Xunyu Zhou, Columbia University, Learning Merton’s Strategies in an Incomplete Market
SAS 1102We study Merton’s expected utility maximization problem in an incomplete market, characterized by a factor process in addition to the stock price process, where all the model primitives are unknown. We take the reinforcement learning (RL) approach to learn optimal portfolio policies directly by exploring the unknown market, without attempting to estimate the model parameters.…