## Number Theory Seminar

**Date: ** January 27, 2022

**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.