# Events for 11/29/2023 from all calendars

## Numerical Analysis Seminar

**Time: ** 3:00PM - 4:00PM

**Location: ** BLOC 302

**Speaker: **Michael Neilan, University of Pittsburg

**Title: ***Divergence-free finite element spaces for incompressible flow on isoparametric meshes*

**Abstract: **In this talk, we construct and analyze an isoparametric and divergence-free finite element pair for the Stokes problem. The pair is defined by mapping the Scott-Vogelius finite element space via a non-traditional Piola transform. The velocity space has the same degrees of freedom as the canonical Lagrange finite element space, and the proposed spaces reduce to the Scott-Vogelius pair in the interior of the domain. The resulting method converges with optimal order, is divergence--free, and is pressure robust. In the second part of the talk, we extend this isoparametric framework to construct a stable and strongly conforming pair. This is achieved by constructing a new divergence-preserving (Piola) mapping combined with an enriching strategy that imposes full continuity across shared edges in the isoparametric mesh.

## Seminar in Random Tensors

**Time: ** 3:00PM - 4:00PM

**Location: ** BLOC 624

**Speaker: **G. Paouris and JM Landsberg, TAMU

**Title: ***Structure v. Randomness III*

## Groups and Dynamics Seminar

**Time: ** 3:00PM - 4:00PM

**Location: ** BLOC 628

**Speaker: **Nataliya Goncharuk, Texas A&M University

**Title: ***Renormalization operators in circle dynamics*

**Abstract: **Renormalization techniques were used in several breakthroughs in circle dynamics.
I will give a short survey of related ideas and results. After that, I will focus on our recent results with M. Yampolsky, with applications to the smoothness of Arnold’s tongues.

## Frontiers in Mathematics

**Time: ** 4:00PM - 5:00PM

**Location: ** Bloc 117

**Speaker: **Frontiers Speaker - Fabrice Baudoin, University of Connecticut

**Description: **Talk 1: Heat flow and sets of finite perimeter
It is well known that among all plane curves, the circle encloses the maximum area for a given perimeter. This question is called the isoperimetric problem in the plane. Mathematicians often generalize problems to encompass broader settings and different levels of abstraction. To effectively address the isoperimetric problem, we require precise definitions of area or volume and perimeter for a set. The rigorous development of these concepts has fueled remarkable advancements in geometric measure theory throughout the 20th and early 21st centuries. Building upon the work of H. Lebesgue (1901-1902), we now have a comprehensive understanding of set volume within the category of measure spaces. The concept of perimeter, however, is more elusive and can be approached from various perspectives. The foundational contributions of R. Caccioppoli (1927-1928) and E. De Giorgi (1950s) have laid the groundwork for our current understanding. This lecture will explore early approaches to the theory of sets of finite perimeter in abstract measure spaces. We will also delve into recent developments of the theory in the context of Dirichlet spaces, where it has been established that a coherent theory of perimeters is intricately linked to fundamental properties of solutions to the heat equation.

## AMUSE

**Time: ** 4:30PM - 6:00PM

**Speaker: **Directed Reading Program, Texas A&M

**Title: ***Final Presentations from Math Directed Reading Program*