## Graduate Number Theory Seminar

This seminar meets weekly and covers all different flavors of Number Theory. We meet Fridays at 1:00-1:50pm in South Hall 4607B, unless noted differently below. If you're interested in attending or giving a talk, or have any questions, contact the organizers, Garo Sarajian, Nadir Hajouji, and David Nguyen.

__Fall 2017 Schedule __

__October 13th__

Speaker: Garo Sarajian

Title: Eratosthenes and the Forty Sieves

Abstract: Sieves are a powerful tool for counting things, from primes to the number of ways to represent integers as sums of primes. In this talk, we'll look at some of the basic ideas of Sieve Theory and discuss different ways to apply these sieves.

__November 3rd__

Speaker: Nadir Hajouji

Title: Intro to Arithmetic of Elliptic Curves

Abstract: I will give an introductory talk to the arithmetic of elliptic curves. I will briefly define elliptic curves, discuss their group structure, show how they give rise to p-adic Galois representations and explain how attempts to computing the group of rational points on an elliptic curve can be obstructed by counterexamples to the Hasse principle.

__December 1st__

Speaker: David Nguyen

Title: The Riemann zeta function and its modern generalizations

Abstract: The classical Riemann zeta function, made famous from Riemann's 1859 memoir, "On the Number of Primes Less Than a Given Magnitude," shed tremendous light on the mysterious distribution of prime numbers. Generalization of the Riemann zeta function began with Dirichlet who used them to prove a deep result on primes in arithmetic progression. In this talk I will survey the classical Riemann zeta function, its modern generalizations, and how they relate to the Langlands conjectures.

__December 8th__

Speaker: Jerry Luo

Title: TBA