Events for 04/16/2024 from all calendars

Nonlinear Partial Differential Equations

Time: 04:00AM - 05:00AM

Location: BLOC 302

Speaker: Angeliki Menegaki , Imperial College London

Title: Non-equilibrium Steady States in a BGK Model for Dilute Gases

Abstract: We study the BGK equation on the 1D torus coupled to a spatially inhomogeneous thermostat, which models heat transfer in gases and remains out of equilibrium due to the action of the thermostat. We study properties of stationary solutions, also known as non-equilibrium steady states. We will discuss the existence, uniqueness and linear dynamical stability of spatially inhomogeneous steady states. This is based on a joint work with Jo Evans (University of Warwick).

Number Theory Seminar

Time: 09:45AM - 10:45AM

Location: BLOC 302

Speaker: Eun Hye Lee, Texas Christian University

Title: Subconvexity of Shintani Zeta Functions

Abstract: Subconvexity problem has been a central interest in analytic number theory for over a century. The strongest possible form of the subconvexity problem is the Lindelof hypothesis, which is a consequence of the RH, in the Riemann zeta function case. There have been many attempts to break convexity for diverse zeta and L functions, usually using the moments method. In this talk, I will introduce the Shintani zeta functions, and present another way to prove a subconvex bound.

Nonlinear Partial Differential Equations

Time: 3:00PM - 4:00PM

Location: BLOC 302

Speaker: Aseel Farhat, Florida State University

Title: Impact of Rotation on the Regularity and Behavior of Navier-Stokes Solutions

Abstract: In this presentation, we will address into the regularity challenges posed by the three-dimensional (3D) Navier-Stokes equations (NSE) and explore the influence of planetary rotation. Additionally, we will discuss an upper bound on the Hausdorff dimension of the global attractor associated with the 2D Navier-Stokes equations on the beta-plane, which depends on the rotation rate (referred to as the Rossby number). Our findings align with outcomes observed in numerical experiments, suggesting that rotation tends to induce a more zonal solution.

Topology Seminar

Time: 4:00PM - 5:00PM

Location: BLOC 302

Speaker: Sara Maloni, University of Virginia

Title: Geometric Structures associated to Higher Teichmüller Theory

Abstract: The Teichmüller space of a surface S is the space of marked hyperbolic structure on S, up to equivalence. By considering the holonomy representation of such structures, this space can also be seen as a connected component of representations from the fundamental group of S into Isom(H^2). Generalizing this point of view, Higher Teichmüller Theory studies connected components of representations from the fundamental group of S into Lie groups of rank greater than 1. We will discuss parts of the classical theory of deformations of geometric structures, Higher Teichmüller Theory and the notion of Anosov representation. We will then describe how Anosov representations correspond to deformation of certain geometric structures, and a joint work with Alessandrini, Tholozan and Wienhard about their topology.