Calendar

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

Informal Geometry and Topology Seminar Questions or comments?

Krishnendu Kar, Louisiana State University
TBD

TBD

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.