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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).

Weekly seminar links:

Number Theory

Faculty with related interests:

Daniel Bump

Professor
Stanford University
Mathematics

Office: 383-U

Address:
450 Serra Mall
Building 380

Phone: (650) 723-4011
Email:
Website: http://math.stanford.edu/~bump/
Research Interests: automorphic forms; Lie groups & representations; number theory

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Brian Conrad

Professor
Stanford University
Mathematics

Office: 383-CC

Address:
450 Serra Mall
Building 380
Stanford, CA 94305-2125

Phone: (650) 723-2972
Email:
Website: http://math.stanford.edu/~conrad
  Research Interests: number theory; arithmetic geometry

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Jacob Fox

Professor
Stanford University
Mathematics

Office: 384-X

Address:
450 Serra Mall
Building 380
Stanford, CA 94305-2125

Phone: (650) 736-6988
Email:
Research Interests: probability; number theory; combinatorics; geometry

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Kemeny, Michael
Szegö Assistant Professor
382-E

Michael Kemeny

Szegö Assistant Professor
Stanford University
Mathematics

Office: 382-E

Address:
450 Serra Mall
Building 380
Stanford, CA 94305-2125

Phone: (650) 721-6799
Email:
Website: http://web.stanford.edu/~mkemeny/homepage.html
Research Interests: algebraic curves & surfaces and their moduli (moduli of singular/smooth curves, syzygies, Brill-Noether theory, K3 surfaces, and Abelian varieties)

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Luk, Jonathan
Assistant Professor
382-Z

Jonathan Luk

Assistant Professor
Stanford University
Mathematics

Office: 382-Z

Address:
450 Serra Mall
Building 380
Stanford, CA 94305-2125

Phone: (650) 723-2209
Email:
Website: http://web.stanford.edu/~jluk/
Research Interests: nonlinear PDE; general relativity; mathematical physics

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Manners, Frederick
Szegö Assistant Professor
382-K

Frederick Manners

Szegö Assistant Professor
Stanford University
Mathematics

Office: 382-K

Address:
450 Serra Mall
Building 380
Stanford, CA 94305-2125

Phone: (650) 723-7824
Email:
Research Interests: number theory; combinatorics

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Ohrt, Christopher
Szegö Assistant Professor
382-Q1

Christopher Ohrt

Szegö Assistant Professor
Stanford University
Mathematics

Office: 382-Q1

Address:
450 Serra Mall
Building 380
Stanford, CA 94305-2125

Phone: (650) 736-1625
Email:
Website: http://web.stanford.edu/~cohrt
Research Interests: differential topology; high torsion invariants

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Kannan Soundararajan

Professor
Stanford University
Mathematics

Office: 383-W

Address:
450 Serra Mall
Building 380
Stanford, CA 94305-2125

Phone: (650) 723-2629
Email:
Website: http://math.stanford.edu/~ksound/
Research Interests: analytical number theory

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Richard Taylor

Professor
Stanford University
Mathematics

Office: 383-T

Address:
450 Serra Mall
Building 380
Stanford, CA 94305-2125

Phone: (650) 497-0640
Email:
Research Interests: algebraic number theory; automorphic forms & Galois reprsentations

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Tsai, Cheng-Chiang
Szegö Assistant Professor
383-BB

Cheng-Chiang Tsai

Szegö Assistant Professor
Stanford University
Mathematics

Office: 383-BB

Address:
450 Serra Mall
Building 380
Stanford, CA 94305-2125

Phone: (650) 723-4080
Email:
Research Interests: representation theory; number theory

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Akshay Venkatesh

Professor
Stanford University
Mathematics

Office: 383-E

Address:
450 Serra Mall
Building 380
Stanford, CA 94305-2125

Phone: (650) 723-4157
Email:
Website: http://math.stanford.edu/~akshay/
Research Interests: number theory; automorphic forms; representation theory

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Walker, Justin
Visiting Scholar
384-E

Justin Walker

Visiting Scholar
Stanford University
Mathematics

Office: 384-E

Address:
450 Serra Mall
Building 380
Stanford, CA 94305-2125

Phone: (650) 736-6998
Email:
Research Interests: number theory

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Zaman, Asif
Postdoctoral Scholar
382-N

Asif Zaman

Postdoctoral Scholar
Stanford University
Mathematics

Office: 382-N

Address:
450 Serra Mall
Building 380
Stanford, CA 94305-2125

Phone: (650) 723-2975
Email:
Website: http://web.stanford.edu/~aazaman/
Research Interests: number theory

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