# Events for 12/03/2018 from all calendars

## Number Theory Seminar

**Time:** 11:00AM - 12:00PM

**Location:** BLOC 220

**Speaker:** Madeline Locus Dawsey, Emory University

**Title:** *Densities of subsets of prime numbers*

**Abstract:** Thanks to the Prime Number Theorem, a lot is known about the distribution of prime numbers. In particular, one can ask whether the methods from analytic number theory yield formulas for densities of subsets of prime numbers. One famous instance of this is the strong form of Dirichlet's famous theorem on primes in arithmetic progressions. Here, we give new formulations of Dirichlet's Theorem, and more generally the Chebotarev Density Theorem, by offering completely new formulas expressing densities of suitable subsets of prime numbers. Our work can be thought of as the non-abelian extension of a theorem of Alladi from the 1970s.

**URL:** *Link*

## Colloquium - Guangbo Xu

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

**Location:** BLOC 220

**Speaker:** Guangbo Xu, Stony Brook University

**Description:** **Title:** Mirror Symmetry and Gauged Linear Sigma Model

**Abstract:** Originally arising from string theory, mirror symmetry has been a fascinating topic in both mathematics and physics for many decades. In this overview talk, I will first briefly explain what mirror symmetry is, and review various mathematical approaches. Then I will explain the mathematical theory of E. Witten's gauged linear sigma model based on my joint project with G. Tian. As an extension of Gromov-Witten theory, our construction settles the mathematical foundation of the approach of K. Hori and C. Vafa towards understanding mirror symmetry.