Contemporary number theory is developing rapidly through its interactions with many other areas of mathematics. Insights from ergodic theory have led to dramatic progress in old questions concerning the distribution of primes, geometric representation theory and deformation theory have led to new techniques for constructing Galois representations with prescribed properties, and the study of automorphic forms and special values of L-functions have been revolutionized by developments in both p-adic and arithmetic geometry as well as in pure representation theory.
The ideas emerging from the Langlands Program (in its many modern guises) and from the developments that grew out of Wiles’ proof of Fermat’s Last Theorem continue to guide much of the ongoing research on the algebraic and geometric sides of the subject, and in the analytic direction the synthesis of additive combinatorics and harmonic analysis continues to lead to breakthroughs in many directions.
In addition to specialized graduate courses, the number theory group has a weekly research seminar with outside speakers from across all areas of number theory. There are also a variety of learning seminars aimed at helping students and postdocs to acquire familiarity with important techniques and results that are generally not available in textbooks (with notes posted for wider dissemination when possible).
Faculty with related interests:
Daniel Bump
ProfessorStanford University
Mathematics
Office: 383-U
Address:
450 Serra Mall
Bldg. 380
Stanford, CA 94305-2125
Phone: (650) 723-4011
Email: bump "at" math.stanford.edu
Website: http://math.stanford.edu/~bump/
Research Interests:
Automorphic forms
Lie groups & representations
Number theory
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Brian Conrad
ProfessorStanford University
Mathematics
Office: 383-CC
Address:
450 Serra Mall
Bldg. 380
Stanford, CA 94305-2125
Phone: (650) 723-2972
Email: conrad "at" math.stanford.edu
Website: http://math.stanford.edu/~conrad
Research Interests:
Number theory
Arithmetic geometry
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Kannan Soundararajan
ProfessorStanford University
Mathematics
Office: 383-W
Address:
450 Serra Mall
Bldg. 380
Stanford, CA 94305-2125
Phone: (650) 723-2629
Email: ksound "at" math.stanford.edu
Website: http://math.stanford.edu/~ksound/
Research Interests:
Analytical Number theory
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Akshay Venkatesh
ProfessorStanford University
Mathematics
Office: 383-E
Address:
450 Serra Mall
Bldg. 380
Stanford, CA 94305-2125
Phone: (650) 723-4157
Email: akshay "at" math.stanford.edu
Website: http://math.stanford.edu/~akshay/
Research Interests:
number theory
automorphic forms
representation theory
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Zhiwei Yun
Associate ProfessorStanford University
Mathematics
Office: 383-BB
Address:
450 Serra Mall
Bldg. 380
Stanford, CA 94305-2125
Phone: (650) 723-4080
Email: zwyun "at" math.stanford.edu
Website: http://web.stanford.edu/~zwyun/
Research Interests:
Geometric Representation Theory
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