Fall 2024 Beginning of Semester Meeting
SAS 4201We will have Howling Cow ice cream at 3:45 in SAS 4104. The departmental meeting will start at 4:15pm in SAS 4201.
Events
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Computational and Applied Mathematics: Daniel Serino, Los Alamos National Lab, Structure-Preserving Machine Learning for Dynamical Systems
ZoomDeveloping 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 CampusI 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 4201Conventional 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…
Geometry and Topology Seminar: James Kolesar, NC State, Shape Optimization and the First Laplace Eigenvalue
SAS 4201In this talk, I will explore the relationship between a domain's shape and its first Laplace eigenvalue, with emphasis on the domains which minimize, or are more generally critical points, for this eigenvalue, for their given volume.
Algebra and Combinatorics Seminar: Corey Jones, NC State, An algebraic approach to discrete quantum field theories
SAS 4201We 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 306Malaria 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 4201The 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 2202This 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…
Stochastics and Discrete Analysis Seminar: José Madrid, Virginia Tech, Convolution Inequalities and Applications
SAS 4201In this talk we will discuss a collection of convolution inequalities for real valued functions on the hypercube, motivated by combinatorial applications. Speaker's website: https://sites.google.com/site/joseramonmadridpadilla/home
Applied Math Graduate Student Seminar: Nikki Xu, NC State, Modeling in Reinforcement Learning for Robust Control
SAS 4201Optimal 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 2106Integrable 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…
Geometry and Topology Seminar: Hunter Stufflebeam, University of Pennsylvania, Stability and Scalar Curvature Lower Bounds
SAS 4201In recent years much attention has turned to rigidity, and almost-rigidity, problems involving lower scalar curvature bounds. In this talk, I'll discuss some contributions to this area, including some new stability theorems for spheres. Some of this is joint work with Davi Maximo, and some is joint with Paul Sweeney Jr.
Algebra and Combinatorics Seminar: Philip Tosteson, UNC Chapel Hill, Representations of categories of finite sets
SAS 4201A 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,…
Math Department Weekly Tea
SAS 4104Differential Equations and Nonlinear Analysis Seminar: Giovanni Gravina, Temple University, Collision and self-contact for viscoelastic solids with Lipschitz boundaries
ZoomIn 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 4201Symmetry 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: Isabella Khan, Princeton, Koszul duality for partial Heegaard diagrams
SAS 4201By slicing a Heegaard diagram for a knot K in $S^3$, it is possible to retrieve the knot Floer homology of K as a tensor product of bimodules over an $\A_{\infty}$ algebra corresponding to the slice. The first step in this process is to assign an $\mathcal{A}_{\infty}$ algebra to this slice, which can also be…
Triangle Topology Seminar: Lisa Piccirillo UT Austin, New constructions and invariants of exotic 4-manifolds.
SAS 4201Dimension 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 4201Multiple 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…