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.
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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
Daniel Kriz Number Theory, Arithmetic Geometry, Iwasawa Theory
Jonathan Wang Geometric Representation Theory, Automorphic Forms, Langlands Program
Researchers & Visitors
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*
*Only a partial list of graduate students