Calendar

Posted March 30, 2026

Probability Seminar Questions or comments?

Olga Iziumtseva, University of Nottingham
Self-intersection local times of Volterra Gaussian processes in stochastic flows with interaction

In this talk, we discuss the existence of multiple self-intersection local times for stochastic processes $x(u(s),t), s\in [0,1]$, where $u$ is a Volterra Gaussian process and $x$ is the solution to the equation with interaction driven by the occupation measure of the process $u$. It appears that self-intersection local times for the process $x(u(s),t), s\in[0,1]$ can be defined as weighted self-intersection local times for the process $u$. We present conditions on Volterra Gaussian processes and weight functions sufficient for the existence of weighted self-intersection local times for a large class of unbounded weights. This is a joint work with Wasiur R. Khudabukhsh

Posted March 27, 2026
Last modified March 30, 2026

Informal Analysis Seminar Questions or comments?

Jai Tushar, Louisiana State University
Polytopal finite element methods

Many problems in science and engineering are modelled by partial differential equations, but solutions are often impossible to compute analytically. One of the most successful tools to numerically approximate such solutions of such problems in one, two and three spatial dimensions are the Finite Element Methods (FEMs). FEM approximates the unknown solution over the domain by subdividing the domain into smaller, simpler pieces called finite element. Traditionally these pieces are simple shapes such as triangles/tetrahedra or quadrilaterals/hexahedra. But in many applications, it is useful to allow more general shapes. In this talk, I will give an informal introduction to the design and analysis of polytopal FEMs, where the computational mesh is made of general polytogonal/polyhedral elements.

Posted January 15, 2026
Last modified March 30, 2026

Informal Geometry and Topology Seminar Questions or comments?

Krishnendu Kar, Louisiana State University
An odd Khovanov stable homotopy type

Khovanov homology admits two integral variants: the original (“even”) theory and the Ozsváth–Rasmussen–Szabó (“odd”) refinement. While both categorify the Jones polynomial and agree over \mathbb{F}_2, their algebraic structures differ in subtle ways. In this talk, I will survey homotopy-theoretic refinements of Khovanov homology, focusing on the Lipshitz–Sarkar stable homotopy type and its odd analogue. I will explain how these spectra are constructed from Burnside categories and homotopy colimits, compare key structural features of the even and odd theories, and discuss their relationship.

Posted March 1, 2026
Last modified March 26, 2026

Harmonic Analysis Seminar

Simon Bortz, University of Alabama
Parabolic Quantitative Rectifiability, Singular Integrals, and PDEs

I will discuss the origins of quantitative rectifiability, starting with the Littlewood–Paley g-function and the Fefferman–Stein characterization of BMO via Poisson extensions. From this point of view, I will describe some of the motivations behind the David–Semmes characterization of uniform rectifiability in terms of Jones’ $L^2$ beta numbers. I will then discuss my work establishing parabolic analogues of some of the equivalences proved by David and Semmes in the elliptic setting, as well as related work by others. I will conclude with recent work connecting this theory to the Dirichlet problem for the heat equation and to quantitative properties of caloric functions.

Posted March 17, 2026
Last modified March 30, 2026

Algebra and Number Theory Seminar Questions or comments?

Shahriyar Roshan-Zamir, Tulane University
Interpolation in Weighted Projective Spaces

Over an algebraically closed field, the double point interpolation problem asks for the vector space dimension of the projective hypersurfaces of degree d singular at a given set of points. After being open for 90 years, a series of papers by J. Alexander and A. Hirschowitz in 1992--1995 settled this question in what is referred to as the Alexander-Hirschowitz theorem. In this talk, we primarily use commutative algebra to prove analogous statements in the weighted projective space, a natural generalization of the projective space. For example, we introduce an inductive procedure for weighted projective space, similar to that originally due to A. Terracini from 1915, to demonstrate an example of a weighted projective plane where the analogue of the Alexander-Hirschowitz theorem holds without exceptions and prove our example is the only such plane. Furthermore, Terracini's lemma regarding secant varieties is adapted to give an interpolation bound for an infinite family of weighted projective planes. There are no prerequisites for this talk besides some elementary knowledge of algebra.

Event contact: Gene Kopp