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Differential Equations and Nonlinear Analysis Seminar: Russell Luke, Universität Göttingen, Inconsistent Nonconvex Feasibility – Foundations and Application to Orbital Tomography

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Feasibility models are a powerful approach to many real-world problems where simply finding a point that comes close enough to meeting many, sometimes contradictory demands is enough. In this talk I will outline the theoretical foundations for the convergence analysis of fixed point iterations of expansive mappings, and show how this specializes to fundamental algorithms…

Teaching and Learning Seminar: Rani Satyam, VCU, Affect Graphing: Tool for understanding students’ confidence, emotion, and experience

SAS 4201

Affect (e.g., beliefs, attitudes, emotions) plays a crucial role in mathematics learning, but reliance on verbal and written responses (from surveys, interviews, etc.) can limit students’ expression of their affective states. As a complement to existing methods, we explore how asking students to graph their affect can be used to study their mathematical experiences. I…

Computational and Applied Mathematics Seminar: Hongkai Zhao, Duke University, Numerical understanding of neural networks: from representation to learning dynamics

SAS 4201

In this talk we present both numerical analysis and experiments to study a few basic computational issues in practice: (1) the numerical error one can achieve given a finite machine precision, (2) the learning dynamics and computation cost to achieve a given accuracy, and (3) stability with respect to perturbations. These issues are addressed for…

Applied Math Graduate Student Seminar: Abhijit Chowdhary, NC State, PyOED: An Open Source, Backend-Agnostic, Bayesian OED Toolbox for Rapid Development

SAS 4201

PyOED is a highly extensible scientific package that enables developing and testing model-constrained optimal experimental design (OED) for inverse problems. Specifically, PyOED aims to be a comprehensive Python toolkit for model-constrained OED. The package targets scientists and researchers interested in understanding the details of OED formulations and approaches. It is also meant to enable researchers…

Biomathematics Seminar: Caroline Moosmueller, UNC, Optimal transport for point-cloud data analysis with applications in biology

Cox 306

This talk will focus on point-cloud data, their analysis and biological applications in which they naturally arise. In particular, I will introduce "optimal transport", which has evolved as one of the major frameworks to meaningfully compare point-cloud data and explain how it can be incorporated into classical machine learning algorithms for further downstream analysis. This…

Algebra and Combinatorics Seminar: Kailash Misra, NC State, Weight multiplicities of some affine Lie algebra modules

SAS 4201

Consider the affine Lie algebra $\mathfrak{g}$ associated with the simple Lie algebra $sl(n)$ consisting of $n\times n$ trace zero matrices over the field of complex numbers. For every dominant integral weight $\lambda$ there is a unique (upto isomorphism) irreducible highest weight $\mathfrak{g}$ module $V(\lambda)$. Although there are infinitely many weights of this module, certain important…

Differential Equations and Nonlinear Analysis Seminar: Ming Chen, University of Pittsburgh, Global bifurcation for hollow vortex desingularization

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A 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 4201

Physics-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 4201

We 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…

Differential Equations and Nonlinear Analysis Seminar: Hakima Bessaih, FIU, Various numerical scheme for stochastic hydrodynamic models

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We 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…

Geometry and Topology Seminar: Peter J. Olver, University of Minnesota, Structure and Generators of Differential Invariant Algebras

SAS 1216

The 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 4201

Global 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…

Geometry and Topology Seminar: Adam Lowrance, Vassar College, The average value of invariants of 2-bridge knots.

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We 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…