We discuss extensions of several inequalities in harmonic analysis to the setting of families of orthonormal functions. While the case of Sobolev-type inequalities is classical, newer results concern the Strichartz…
This work explores the recovery stochastic volatility models (SVMs) from market models for the VIX futures term structure. Market models have more flexibility for fitting of curves than do SVMs,…
The study of extremals for Steklov eigenvalues has revitalised the theory of free boundary minimal surfaces. One of the most basic open questions can be phrased as follows: Can a…
Factor systems are a tool for working on the extension problem for algebraic structures such as groups, Lie algebras, and associative algebras. We construct the Leibniz algebra analogue to a…
We consider the restriction to the unit circle of random degree-n polynomials with iid coefficients (Kac polynomials). Recent work of Yakir and Zeitouni shows that for Gaussian coefficients, the minimum…
In this talk, we will explain a (mysterious?) connection between the combinatorics of affine buildings and representation theory in type A. If a group acts simply and transitively on the…
In my talk, I will explain the approach of finding solutions to nonlinear PDEs via tug-of-war games. I will focus on the context of p-Laplacian and the non-local geometric p-Laplacian.…
A curve of constant width has the property that any two parallel supporting lines are the same distance apart in all directions. A fundamental problem involving these curves is to…
Chair: Alen Alexanderian (alexanderian@ncsu.edu, contact for Zoom access)
Zoom ID: 939 3643 7199 (opens 15 min prior to the meeting) Passcode: 9917
In a Hilbert space, for convex optimization, we report on recent advances regarding the acceleration of first-order algorithms. We rely on inertial dynamics with damping driven by the Hessian, and…
This is a report on the joint work with Matthew Levy. We use surjection operations on integral cochains tof a topological space X (described by McClure-Smith and Berger-Fresse) to describe…
An important problem in computer vision is to understand the space of images that can be captured by an arrangement of cameras. A description of this space allows for statistical…
Let X and Y be random variables. Quasi-independence models are log-linear models that describe a situation in which some states of X and Y cannot occur together, but X and…
Suppose we model n votes in an election between two candidates as n i.i.d. uniform random variables in {-1,1}, so that 1 represents a vote for the first candidate, and…
We consider a finite group scheme G, and its associated representation category rep G. Here one can think of a finite discrete group, or an infinitesimal group scheme, such as…
We survey the known results concerning the minimal Riesz energy on sufficiently smooth sets, and present some new results on fractal sets, which are the key examples of non-rectifiable sets.…
The Ricci curvature Ric(g) is a symmetric 2-tensor on a Riemannian manifold (M,g) that encodes curvature information. It features in several interesting geometric PDEs such as the Ricci flow and the Einstein equation.…