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Differential 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…
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…
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…
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…
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…
Pure Math Graduate Student Seminar: Reeshad Arian, NC State, Quandles and Knots
SAS 2106A 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…
Geometry Topology Seminar: Tye Lidman, NC State, 3-manifolds in symplectic 4-manifolds
SAS 4201Symplectic 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…
Algebra and Combinatorics Seminar: Sean Thompson, NC State, Quiver connections and bimodules of basic algebras
SAS 4201Motivated 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…
Math Department Weekly Tea
SAS 4104Computational and Applied Mathematics: Erik Bollt, Clarkson University, Next-Generation Reservoir Computing, and On Explaining the Surprising Success of a Random Neural Network for Forecasting Chaos
SAS 4201Machine learning has become a widely popular and successful paradigm, including for data-driven science. A major application is forecasting complex dynamical systems. Artificial neural networks (ANN) have evolved as a…
Stochastics and Discrete Analysis Seminar: Zoe Huang, UNC Chapel Hill, Cutoff for random Cayley graphs of nilpotent groups
SAS 4201We consider the random Cayley graphs of a sequence of finite nilpotent groups of diverging sizes G = G(n), whose ranks and nilpotency classes are uniformly bounded. For some k…
Applied Mathematics Graduate Student Seminar: James Garrison, NC State, Randomized Preconditioned Cholesky-QR in Mixed Precision
SAS 4201We analyze a randomized preconditioned Cholesky-QR algorithm for computing the thin QR factorization of real matrices with full rank. Using a perturbation analysis that is transparent and identifies clearly all…
Pure Math Graduate Student Seminar: Everett Meike, NC State, Cataloguing 2-adjacent knots
SAS 2106Generalizing unknotting number, n-adjacent knots have n crossings such that changing any non-empty subset of them results in the unknot. We determine the 2-adjacent knots through 12-crossings, with one exception.…
Geometry and Topology Seminar: Eric Hanson, NC State, Topological data analysis via relative homological algebra
SAS 4201One of the main approaches to topological data analysis is to study discrete invariants of (multiparameter) persistence modules. In this talk, we discuss recent research which utilizes techniques from (relative)…
Algebra and Combinatorics Seminar: Nick Mayers, NC State, The quantum k-Bruhat order
SAS 4201Finding combinatorial interpretations for the structure constants of Schubert polynomials is a long-standing open problem in algebraic combinatorics. In the case where one of the Schubert polynomials is a Schur…
Differential Equations and Nonlinear Analysis Seminar: Jone Apraiz, Universidad del País Vasco, Inverse problem for a one-dimensional fluid-solid interaction model
ZoomIn this talk we will first briefly review some geometric inverse problems we have studied for the one-dimensional heat, wave and Burgers equations. Then, we will consider a one-dimensional fluid-solid…
Computational and Applied Mathematics: Isaac Harris, Purdue University, Transmission Eigenvalue Problems for a Scatterer with a Conductive Boundary
SAS 4201In this talk, we will investigate the acoustic transmission eigenvalue problem associated with an inhomogeneous media with a conductive boundary. These are a new class of eigenvalue problems that are…
Colloquium: Bojko Bakalov, NC State, Dynamical Lie algebras
SAS 4201Quantum computers are physical machines that process information using the principles of quantum mechanics, which in turn is underpinned by linear algebra. The talk will start with a review of…