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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

Zoom

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…

Triangle Topology Seminar: Lisa Piccirillo UT Austin, New constructions and invariants of exotic 4-manifolds.

SAS 4201

Dimension four is the lowest dimension where smooth and topological manifolds can differ; any difference between these categories is known as exotica. In particular, a smooth 4-manifold is \emph{exotic} if there is another smooth 4-manifold which is homeomorphic but not diffeomorphic to it. There is a wealth of literature, mostly written between 1983 and 2008,…

Stochastics and Discrete Analysis Seminar: Andrew Papanicolaou, NC State, Principal Eigenportfolios and Primary Factors

SAS 4201

Multiple financial assets’ time-series data is stored in a matrix upon which we perform principal component analysis to find predominant factors in the market. Random matrix theory helps us to identify the number of factors present in the data, with the top eigenvalue-eigenvector pair bearing a strong resemblance to the market’s capitalization-weighted portfolio. This resemblance…

Pure Math Graduate Student Seminar: Reeshad Arian, NC State, Quandles and Knots

SAS 2106

A fundamental problem in knot theory is determining when two distinct knot diagrams represent the same knot. This is traditionally addressed through the use of invariants such as the knot group, Alexander polynomial, and Jones polynomial, among others. While the knot group distinguishes prime knots, it is known to be incomplete as a knot invariant.…

Geometry Topology Seminar: Tye Lidman, NC State, 3-manifolds in symplectic 4-manifolds

SAS 4201

Symplectic manifolds show up in many areas of mathematics, including topology, geometry, representation theory, and dynamics. In the talk I will give an introduction to symplectic manifolds and then discuss embeddings of 3-manifolds into symplectic 4-manifolds. This is joint work with Ali Daemi and Mike Miller Eismeier.

Algebra and Combinatorics Seminar: Sean Thompson, NC State, Quiver connections and bimodules of basic algebras

SAS 4201

Motivated by the problem of classifying quantum symmetries of non-semisimple, finite-dimensional associative algebras, we define a notion of connection between bounded quivers and build a bicategory of bounded quivers and quiver connections. We prove this bicategory is equivalent to a bicategory of basic algebras,  bimodules, and intertwiners with some additional structure. Speaker’s website: https://math.sciences.ncsu.edu/people/sthomps6/