# Number Theory

The integers and prime numbers have fascinated people since ancient times. Recently, the field has seen huge advances. The resolution of Fermat's Last Theorem by Wiles in 1995 touched off a flurry of related activity that continues unabated to the present, such as the recent solution by Khare and Wintenberger of Serre's conjecture on the relationship between mod p Galois representations and modular forms. The Riemann hypothesis, a Clay Millennium Problem, is a part of analytic number theory, which employs analytic methods (calculus and complex analysis) to understand the integers. Recent advances in this area include the Green-Tao proof that prime numbers occur in arbitrarily long arithmetic progressions. The Langlands Program is a broad series of conjectures that connect number theory with representation theory. Number theory has applications in computer science due to connections with cryptography.

The research interests of our group include Galois representations, Shimura varieties, automorphic forms, lattices, algorithmic aspects, rational points on varieties, and the arithmetic of K3 surfaces.

## Home Site

## Faculty

Henry Cohn
*Discrete Mathematics*

Bjorn Poonen
*Number Theory, Algebraic Geometry*

Andrew Sutherland
*Computational Number Theory and Arithmetic Geometry*

Zhiwei Yun
*Geometric Representation Theory, Number Theory*

Wei Zhang
*Number Theory, Automorphic Forms, Algebraic Geometry*

## Instructors & Postdocs

Aaron Landesman
*Classical algebraic geometry, moduli spaces, arithmetic statistics, monodromy, mapping class groups*

Yujie Xu
*Arithmetic Geometry, Number Theory and Representation Theory*

## Researchers & Visitors

Shiva Chidambaram
*Algebraic number theory, abelian varieties, Galois representations, arithmetic geometry*

Edgar Costa
*Computational Number Theory, Arithmetic Geometry*

David Roe
*Computational number theory, Arithmetic geometry, local Langlands correspondence*

Raymond van Bommel
*Computational Number Theory, Arithmetic Geometry*

## Graduate Students*

Xunjing Wei
*Number theory, Representation theory*

*Only a partial list of graduate students