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Representation theory is fundamental in the study of objects with symmetry. It arises in contexts as diverse as card shuffling and quantum mechanics. An early success was the work of Schur and Weyl, who computed the representation theory of the symmetric and unitary groups; the answer is closely related to the classical theory of symmetric functions and deeper study leads to intricate questions in combinatorics.

More recently, methods from geometry and topology have greatly enhanced our understanding of these questions (“geometric representation theory”).¬†The study of affine Lie algebras and quantum groups has brought many new ideas and viewpoints, and representation theory now furnishes a basic language for other fields, including the modern theory of automorphic forms.

All of these aspects are studied by Stanford faculty.  Topics of recent seminars include combinatorial representation theory as well as quantum groups.

Weekly seminar links:

Representation Stability Reading Group

Faculty with related interests:

Daniel Bump

Professor
Stanford University
Mathematics

Office: 383-U

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

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

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Church, Tom
Assistant Professor
383-Y

Tom Church

Assistant Professor
Stanford University
Mathematics

Office: 383-Y

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

Phone: (650) 725-8572
Email:
Website: http://math.stanford.edu/~church/
Research Interests: topology, especially low-dimensional topology

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Diaconis, Persi
Mary V. Sunseri Professor of Statistics and Mathematics
383-D

Persi Diaconis

Mary V. Sunseri Professor of Statistics and Mathematics
Stanford University
Mathematics and Statistics

Office: 383-D

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

Phone: (650) 723-5183
Email:
Website: http://statweb.stanford.edu/~cgates/PERSI/index.html
Research Interests: Probability Combinatorics Statistics Group 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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