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Algebra and Combinatorics Seminar: Apoorva Khare, Indian Institute of Science (Bangalore, India), Schur polynomials: from smooth functions to symmetric function identities

SAS 1102

Cauchy's determinantal identity (1840s) expands via Schur polynomials the determinant of the matrix f, where f(t) = 1/(1-t) is applied entrywise to the rank-one matrix u v^T = (u_i v_j). This theme has resurfaced in the 2010s in analysis (following a 1960s computation by Loewner), in the quest to find polynomials p(t) with a negative coefficient that entrywise preserve…

Biomathematics Seminar: Orlando Arguello-Miranda, Department of Plant and Microbial Biology at NC State, Deep learning and the yet-to-be-discovered mathematical principles of biology

Cox 306

Biology is defined by non-linear reactions caused by numerous molecular components interacting inside living cells. The complexity of such systems has limited classical experimental approaches in their capacity to measure living biological networks. This talk will explore how new computational tools derived from artificial intelligence are currently applied to study complex biological networks in living…

Geometry and Topology: Teemu Saksala, NC State, Hyperbolic inverse problems with time dependent and time independent coefficients

SAS 4201

In this talk we will discuss the differences in the methodology of determining time-dependent and time-independent coefficients appearing in a hyperbolic equation in a Riemannian manifold. The talk is based on two recent research projects: 1) We will prove that a local source-to-solution map of a hyperbolic partial differential operator on a complete Riemannian manifold (no…

Computational and Applied Mathematics: Daniel Serino, Los Alamos National Lab, Structure-Preserving Machine Learning for Dynamical Systems

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Developing robust and accurate data-based models for dynamical systems originating from plasma physics and hydrodynamics is of paramount importance. These applications pose several challenges, including the presence of multiple scales in time and space and a limited number of data, which is often noisy or inconsistent. The aim of structure-preserving ML is to strongly enforce…

Department of Mathematics Fall Picnic

The Corner at Centennial Campus

I wanted to invite all of you to our Department of Mathematics Fall Picnic.  We will be holding it at The Corner on Centennial Campus from 12-2 pm on August 24th.  We look forward to seeing you and hope you will then take advantage of going to Packapalooza on Hillsborough Street from 2-10pm. Please sign…

Stochastics and Discrete Analysis Seminar: Michael Hott, University of Minnesota, On the quest for superconductivity in Twisted Bilayer Graphene

SAS 4201

Conventional superconductivity emerges for weakly interacting Fermi gases, and its emergence has been studied in mathematical physics. Such conventional superconductors, however, have a very low critical temperature, making them very expensive in applications. Unconventional superconductors, such as cuperates, on the other hand exhibit a very high critical temperature, but we have very little understanding of…

Algebra and Combinatorics Seminar: Corey Jones, NC State, An algebraic approach to discrete quantum field theories

SAS 4201

We will give an introduction to nets of associative algebras over discrete metric spaces, which arise in mathematical physics as axiomatizations of the observables content of quantum field theories over discrete spaces. We will present examples arising naturally from combinatorics and representation theory, and discuss some recent structural results about these objects. Speaker's website: https://www.coreyjonesmath.com/

Biomathematics Seminar: Lauren Childs, Department of Mathematics at Virginia Tech, Assessing the Impact of the Wolbachia-Based Control of Malaria

Cox 306

Malaria is a deadly infectious disease causing over 200 million cases and over half a million deaths each year. It is transmitted through the bite of an infectious Anopheles mosquito. Control methods, primarily focused on affecting the ability of the mosquito to bite or transmit the disease by employing insecticides, have reduced the impact of…

Algebra and Combinatorics Seminar: Yairon Cid-Ruiz, NC State, Multiplicities and integral dependence

SAS 4201

The theory of integral closure of ideals, originating in the early twentieth century with work of Krull, Zariski, Rees, and others, remains a vibrant area of research in algebraic geometry, commutative algebra, and singularity theory. This theory's significance partly stems from its connections with numerical invariants such as multiplicities. During the 1950s, significant advances by…

SUM Club: That Time We Discovered the Proof for a Major Open Question in Mathematics in a 4chan Post About Anime from 2011

SAS 2202

This Wednesday, September 4th at 6:00pm SUM Club will be hosting a comedy talk on some quirked up (recent) mathematical history! Our esteemed community coordinator, Quill Nebeker, will be presenting on: “That Time We Discovered the Proof for a Major Open Question in Mathematics in a 4chan Post About Anime from 2011” The meeting will be in…

Applied Math Graduate Student Seminar: Nikki Xu, NC State, Modeling in Reinforcement Learning for Robust Control

SAS 4201

Optimal control designed with reinforcement learning can be sensitive to model mismatch. We demonstrate that designing such controllers in a virtual simulation environment with an inaccurate model is not suitable for deployment in a physical setup. Controllers designed using an accurate model are robust against disturbance and small mismatch between the physical setup and the…

Pure Math Graduate Student Seminar: Jack Reever, The journey to finding an explicit solution to a cross-ratio system

SAS 2106

Integrable cross-ratio maps are solutions to one of the discrete integrable equations on quad-graphs. These maps may be of interest to many mathematicians; just to name a few uses, discrete holomorphic functions, orthogonal circle packings, and polygon recutting are all special cases of integrable cross-ratio maps. The goal of my research is to find an…

Algebra and Combinatorics Seminar: Philip Tosteson, UNC Chapel Hill, Representations of categories of finite sets

SAS 4201

A representation of the category of finite sets is a linear algebraic object, which roughly consists of a sequence of representations V_n of the symmetric group S_n related by transition maps.  These representations occur naturally in several places including in the study of Kazhdan-Lusztig polynomials of braid matroids, the homology of moduli spaces of curves,…

Differential Equations and Nonlinear Analysis Seminar: Giovanni Gravina, Temple University, Collision and self-contact for viscoelastic solids with Lipschitz boundaries

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In this talk, we will examine the time evolution of viscoelastic solids within a framework that allows for collisions and self-contact. In the static and quasi-static regimes, corresponding existence results have been shown through variational descriptions of the problem. For the fully dynamical case, however, collisions have so far either been ignored or handled using…

Computational and Applied Mathematics: Wei Zhu, Georgia Institute of Technology, Symmetry-Preserving Machine Learning: Theory and Applications

SAS 4201

Symmetry is prevalent in a variety of machine learning and scientific computing tasks, including computer vision and computational modeling of physical and engineering systems. Empirical studies have demonstrated that machine learning models designed to integrate the intrinsic symmetry of their tasks often exhibit substantially improved performance. Despite extensive theoretical and engineering advancements in symmetry-preserving machine…