Events for 04/01/2025 from all calendars

Nonlinear Partial Differential Equations

Time: 3:00PM - 4:00PM

Location: Zoom

Speaker: Connor R Mooney , University of California Irvine

Title: Singular solutions to the special Lagrangian equation and the minimal surface system

Abstract: The special Lagrangian equation (SLE) was introduced by Harvey and Lawson in the context of calibrated geometries. We will talk about the construction of singular viscosity solutions to SLE that are Lipschitz but not C^1, and have non-minimal gradient graphs. The singularities are related to certain degenerate Bellman equations and the free boundaries associated with them. We will also discuss a similar construction in the context of the minimal surface system. This is joint work with O. Savin.

Matrix Concentration and Universality - Working Seminar on HDP

Time: 4:30PM - 5:30PM

Location: Blocker 302

Speaker: Tatiana Brailovskaya (Duke)

Description: In the latter half of the 20th century, extending scalar concentration inequalities to arbitrary Banach spaces has gained poplularity due to the implications for local geometry of these spaces. In 1990s, Lust-Piquard and Pisier intiated the study of matrix concentration by proving an analogue of the classical Khintchine inequality for matrices. This non-commutative Khinchine inequality paved the way for investigating spectral properties of random matrices with non-identical, non-independent entries, which are outside of the real of classical random matrix theory. Nowadays, there are numerous applications of matrix concentration in computer science and applied and pure mathematics. In this talk, I will discuss recent results concerning the spectrum of sums of independent random matrices with appropriate control on operator norms.