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Algebra and Combinatorics Seminar: Kyle Celano, Wake Forest University, Chromatic Symmetric Functions and RSK for (3 + 1)-free Posets

SAS 4201

In 1995, Stanley introduced the chromatic symmetric function of a graph, a symmetric function analog of the classical chromatic polynomial of a graph. The Stanley-Stembridge e-positivity conjecture is a long-standing conjecture that states that the chromatic symmetric function of a certain class of graphs, called incomparability graphs of (3+1)-free posets, has nonnegative coefficients when expanded…

Differential Equations and Nonlinear Analysis Seminar: Leon Bungert, University of Würzburg, Adversarial robustness in machine learning: from worst-case to probabilistic

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In this talk I will first review recent results which characterize adversarial training (AT) of binary classifiers as nonlocal perimeter regularization. Then I will speak about a probabilistic generalization of AT which also admits such a geometric interpretation, albeit with a different nonlocal perimeter. Using suitable relaxations one can prove the existence of solutions for…

Teaching and Learning Seminar: Maria Meehan, University College Dublin, Video recordings to complement, or substitute for, the first-year mathematics lecture: One lecturer’s journey

SAS 4201

As part of a professional development project aimed at engaging in the Discipline of Noticing as conceptualised by John Mason, some colleagues and I wrote and shared brief-but-vivid accounts of our practice. Evident in these accounts is the catalyst for the subsequent change in my practice of introducing short, pre-recorded videos to complement, or substitute…

Computational and Applied Mathematics Seminar: Gregory Ongie, Marquette University, A function space view of infinite-width neural networks

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It is well-known that nearly any function can be approximated arbitrarily-well by a neural network with non-linear activations. However, one cannot guarantee that the weights in the neural network remain bounded in norm as the approximation error goes to zero, which is an important consideration when practically training neural networks. This raises the question: What…

Biomathematics Seminar: TBA

Cox 306

All BMA seminars have a virtual option with the following Zoom Link: https://ncsu.zoom.us/j/93046132033?pwd=dkZiTjlKazgzK2Q3aXJra1g2R1Q0dz09 Meeting ID: 930 4613 2033 Passcode: 075251

Differential Equations and Nonlinear Analysis Seminar: Tu Nguyen Thai Son, Michigan State University, Generalized convergence of solutions for nonlinear Hamilton-Jacobi equations

SAS 4201

We examine the asymptotic behaviors of solutions to Hamilton-Jacobi equations while varying the underlying domains. We establish a connection between the convergence of these solutions and the regularity of the additive eigenvalues in relation to the domains. To accomplish this, we introduce a framework based on Mather measures that enables us to compute the one-sided derivative…

Computational and Applied Mathematics Seminar: Antoine Blanchard, Verisk, A Multi-Scale Deep Learning Framework for Projecting Weather Extremes

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Extreme weather events are of growing concern for societies because under climate change their frequency and intensity are expected to increase significantly. Unfortunately, general circulation models (GCMs)--currently the primary tool for climate projections--cannot characterize weather extremes accurately. Here, we report on advances in the application of a multi-scale deep learning framework, trained on reanalysis data,…

Geometry and Topology Seminar: Andrew Shedlock, NC State, Recovery of a complete Riemannian Manifold using the local source-to-solution operator for the Electro-Magnetic Wave Operator

SAS 1216

In this talk we consider an Electro-Magnetic Wave operator on a complete Riemannian manifold, which generalizes the standard wave equation to include first order and zeroth order terms.  The Cauchy Problem for the Electro-Magnetic Wave operator with zero initial values and a smooth compactly supported forcing function has a unique smooth solution. We study the…

Geometry and Topology Seminar: Lili Yan, University of Minnesota, Stable determination of time-dependent collision kernel in the nonlinear Boltzmann equation

SAS 1216

In this talk, we consider an inverse problem for the nonlinear Boltzmann equation with a time-dependent kernel in dimensions 2 and higher. We establish a logarithm-type stability result for the collision kernel from measurements under certain additional conditions. A uniqueness result is derived as an immediate consequence of the stability result. Our approach relies on…

Applied Math Graduate Student Seminar: Sam Thornton, NC State, Dual-Domain Clustering of Spatiotemporal Infectious Disease Data

SAS 4201

The purpose of this project is to develop, test, and document performance of dual-domain clustering algorithms for spatiotemporal datasets, tailored to pandemic preparedness and endgame challenges. Dual-domain clustering refers to the unsupervised learning clustering method performed on data with both application-specific attributes (e.g., number of infectious) and geographic information (e.g., latitude and longitude of data…

Colloquium: Christopher K.R.T. Jones, University of North Carolina at Chapel Hill, Do We Need to Adapt to a Changing Climate, or to the Rate at Which it is Changing?

SAS 4201

The climate is changing due to the heat trapping caused by the rapid increase in greenhouse gases, mainly carbon dioxide, in the atmosphere. One way to state the issue is that we cannot, as a species, adapt to the new conditions quickly enough. This is an example of rate-induced tipping for which the mathematics has…

Algebra and Combinatorics Seminar: Raymond Maresca, Brandeis University, Combinatorics of exceptional collections in type A-tilde

SAS 4201

We will define quivers of type A-tilde, their representations, and exceptional collections of these representations. We will then introduce a combinatorial model of these representations, based on the one constructed by Garver, Igusa, Matherne, and Ostroff for type A, by drawing strands on a copy of the integers. We will see that collections of strands…

Differential Equations and Nonlinear Analysis Seminar: Anna Doubova, University of Seville, Inverse problems connected with Burgers equation and some related systems

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We consider inverse problems concerning the one-dimensional viscous Burgers equation and some related nonlinear systems (involving heat effects, variable density, and fluid-solid interaction). We are dealing with inverse problems in which the goal is to find the size of the spatial interval from some appropriate boundary observations. Depending on the properties of the initial and…

Computational and Applied Mathematics Seminar: Gabriel P. Langlois, Courant Institute, An exact and efficient algorithm for the Lasso regression problem based on a Hamilton-Jacobi PDE formulation

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The Basis Pursuit Denoising problem, also known as the least absolute shrinkage and selection operator (Lasso) problem, is a cornerstone of compressive sensing, statistics and machine learning. In high-dimensional problems, recovering an exact sparse solution requires robust and efficient optimization algorithms. State-of-the-art algorithms for the Basis Pursuit Denoising problem, however, were not traditionally designed to…

Stochastics Seminar: Erik Bates, NC State, The Busemann process of (1+1)-dimensional directed polymers

SAS 4201

Directed polymers are a statistical mechanics model for random growth.  Their partition functions are solutions to a discrete stochastic heat equation.  This talk will discuss their logarithmic derivatives, which are solutions to a discrete stochastic Burgers equation.  Of interest is the success or failure of the  "one force-one solution principle" for this equation.  I will…

Stochastics Seminar: Evan Sorensen, Columbia University, Jointly invariant measures for the Kardar-Parisi-Zhang Equation

SAS 4201

We give an explicit description of the jointly invariant measures for the KPZ equation. These are couplings of Brownian motions with drift, and can be extended to a process defined for all drift parameters simultaneously. We term this process the KPZ horizon (KPZH). As a corollary of this description, we resolve a recent conjecture of…