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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…

Differential Equations and Nonlinear Analysis Seminar: Edouard Pauwels, Université de Toulouse, Nonsmooth differentiation of parametric fixed points

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Recent 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…

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 4201

In 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 4201

Consider 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…

Algebra and Combinatorics Seminar: Maximilian Kaipel, University of Cologne, Partitioned fans, hyperplane arrangements and K(pi,1) spaces

SAS 4201

Polyhedral 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

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We 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 4201

Spreading (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 1102

We 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.…

Applied Math Graduate Student Seminar: Harley Hanes, NC State, Boundary Penalties, Sensitivity Equation Projection, and Optimal Sample Identification in Reduced-Order Models

SAS 4201

Reduced-order models (ROMs) are a critical tool for sensitivity analysis, parameter inference, and uncertainty quantification where high-fidelity models would be computationally intractable. Galerkin POD-ROMs are one particular class of ROMs which project high-fidelity model equations onto a set of model solutions to construct ROMs retaining original model parameters and physics, enabling accurate sensitivity analysis, parameter inference,…

Biomathematics Seminar: Jichun Xie, Duke, Disentangling Cellular Heterogeneities and Activities from the Topology Structures of Single-cell Co-expression Graphs

Cox 306

Gene co-expression graphs are a rich source of information, revealing critical insights into cellular functions, states, and activities. Yet, extracting meaningful signals from these graphs presents a formidable challenge. This complexity arises due to the presence of multiple, overlapping sources of information and the inherent noise, which is particularly pronounced in data derived from single-cell…

Geometry and Topology Seminar: Salem Selim, UC Irvine, Partial data inverse problems for magnetic Schrödinger operators with potentials of low regularity.

SAS 4201

In this talk we discuss partial data inverse boundary problems for magnetic Schrödinger operators on bounded domains in the Euclidean space as well as some Riemannian manifolds with boundary. In particular, we show that the knowledge of the set of the Cauchy data on a portion of the boundary of a domain in the Euclidean…