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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Department Members in This Field
Faculty
- Henry Cohn Discrete Mathematics
- Bjorn Poonen Arithmetic Geometry, Algebraic Number Theory, Rational Points on Varieties, Undecidability
- Andrew Sutherland Computational Number Theory and Arithmetic Geometry
- Zhiwei Yun Representation Theory, Number Theory, Algebraic Geometry
- Wei Zhang Number Theory, Automorphic forms, Arithmetic Geometry
Instructors & Postdocs
- Patrick Bieker Arithmetic Geometry, Langlands Program
- Aaron Landesman Classical algebraic geometry, moduli spaces, arithmetic statistics, monodromy, mapping class groups
- Thomas Rüd Number theory, representation theory of p-adic groups, algebraic geometry
- Robin Zhang Number Theory, Automorphic Forms, Arithmetic Geometry
- Nina Zubrilina Number Theory, Modular Forms
Researchers & Visitors
- Edgar Costa Computational Number Theory, Arithmetic Geometry
- David Roe Computational number theory, Arithmetic geometry, local Langlands correspondence
- Samuel Schiavone Computational number theory, arithmetic geometry
Graduate Students*
- Niven Achenjang
- Ryan Chen Number Theory, Arithmetic Geometry
- Evan Chen Number theory, combinatorics
- Weixiao Lu
- Mikayel Mkrtchyan
- Ayan Nath
- Hao Peng
- Jia (Jane) Shi
- Vijay Srinivasan
- Zeyu Wang
*Only a partial list of graduate students