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Differential Equations and Nonlinear Analysis Seminar: Ming Chen, University of Pittsburgh, Global bifurcation for hollow vortex desingularization
ZoomA hollow vortex is a region of constant pressure bounded by a vortex sheet and suspended inside a perfect fluid; we can think of it as a spinning bubble of air in water. In this talk, we present a general method for desingularizing non-degenerate steady point vortex configurations into collections of steady hollow vortices. The…
Computational and Applied Mathematics Seminar: Vakhtang Putkaradze, University of Alberta, Lie-Poisson Neural Networks (LPNets): Data-Based Computing of Hamiltonian Systems with Symmetries
SAS 4201Physics-Informed Neural Networks (PINNs) have received much attention recently due to their potential for high-performance computations for complex physical systems, including data-based computing, systems with unknown parameters, and others. The idea of PINNs is to approximate the equations and boundary and initial conditions through a loss function for a neural network. PINNs combine the efficiency…
Stochastics Seminar: Sayan Banerjee , UNC-Chapel Hill, Ergodicity and fluctuations of the Atlas model
SAS 4201We investigate the long-time behavior and stationary fluctuations of an infinite-dimensional rank-based diffusion process, called the Atlas model, where particles move as independent Brownian motions, with the lowest ranked particle at any time getting a unit upward drift. The associated process of gaps between successive ranked particles possesses an uncountable collection of invariant measures. We…
Biomathematics Seminar: Veronica Ciocanel, Duke, TBA
Cox 306Speaker's website Zoom Link
Algebra and Combinatorics Seminar: Spencer Daugherty, NC State, Thesis Defense
SAS 4201Speaker’s webpage: https://spdaugherty.github.io/
Math Department Weekly Tea
SAS 4104Differential 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