Events for 01/27/2022 from all calendars

Number Theory Seminar

Time: 10:00AM - 11:00AM

Location: BLOC 302

Speaker: Matt Young, Texas A&M University

Title: Large sieve inequalities for families of automorphic forms

Abstract: The classical large sieve inequality for Dirichlet characters has arithmetical interest because of its applications to the distribution of primes in arithmetic progression, and to more general sieve problems. One can view this classical result as a large sieve inequality for the family of GL_1 automorphic forms, and it is desirable to extend this to more general families. The quality of a large sieve inequality for a family of automorphic forms (or L-functions) is a tangible way to measure how well the family is understood. For many GL_1 and GL_2 families, we have optimal large sieve inequalities; the GL_1 family is the classical large sieve, and many GL_2 families are covered by work of Deshouillers-Iwaniec. In higher rank, our knowledge is highly incomplete. In this talk, I will discuss some recent progress on a GL_3 family.

Colloquium - Visu Makam

Time: 11:30AM - 12:30PM

Location: ZOOM

Speaker: Visu Makam, University of Melbourne, Australia

Description:
Title: Interactions between invariant theory and complexity theory
Abstract: Invariant theory and complexity theory are two fundamental subjects in algebra and theoretical computer science respectively. The two subjects have found common ground in the past two decades due to some spectacular discoveries that place invariant theory and representation theory at the forefront of some of the central open problems in complexity theory such as identity testing and even the celebrated P vs NP problem. In this talk, I will present my perspective of this young and rapidly developing field. I will emphasize new research directions in invariant theory motivated by investigations in complexity theory and how various results in invariant theory can inform and evolve our understanding of complexity theory. I will draw upon results from joint works with several collaborators and showcase some results with a view towards the future of the subject.

Colloquium - Yuwen Li

Time: 4:00PM - 5:00PM

Location: BLOC 117

Speaker: Yuwen Li, Pennsylvania State University

Description:
Title: Preconditioning in H(curl) and H(div)
Abstract: Preconditioning is widely used for efficiently solving large-scale systems of linear equations. In the first part of my talk, I will present a novel application of preconditioning and derive a posteriori error estimates of finite element methods in H(curl) and H(div) using preconditioning theory. In the second part, I will show new user-friendly preconditioners for solving discrete H(curl) and H(div) systems on triangulated surfaces. Part of this talk is based on joint work with Ludmil Zikatanov.