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Topology studies properties of spaces that are invariant under deformations. A special role is played by manifolds, whose properties closely resemble those of the physical universe. Stanford faculty study a wide variety of structures on topological spaces, including surfaces and 3-dimensional manifolds. The notion of moduli space was invented by Riemann in the 19th century to encode how Riemann surfaces vary in families; today, the study of geometric and homotopy-theoretic aspects of moduli spaces is an important subject with strong ties to algebraic and symplectic geometry. It also leads to interesting dynamical systems and group theory. More algebraic aspects of topology study homotopy theory and algebraic K-theory, and their applications to geometry and number theory.

The topology group offers regular first- and second-year graduate classes, as well as specialized courses on varying topics. In addition, there are two weekly seminars with outside invited speakers, as well as several learning seminars run by faculty and graduate students.

Weekly seminar links:

Topology

Student Topology

Topology Progress

Informal Geometry & Topology

Gunnar Carlsson

Professor Emeritus
Stanford University
Mathematics

Office: 383-L

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

Phone: (650) 723-2224
Email:
Website: http://math.stanford.edu/~gunnar/
Research Interests: Algebraic topology Algebraic K-theory 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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Cohen, Ralph
Barbara Kimball Browning Professor in the School of Humanities and Sciences
383-X

Ralph Cohen

Barbara Kimball Browning Professor in the School of Humanities and Sciences
Stanford University
Mathematics

Office: 383-X

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

Phone: (650) 723-1862
Email:
Website: http://math.stanford.edu/~ralph/

 

Awards:

    Bass University Fellow in Undergraduate Education

 

    Professor of Mathematics
    Senior Associate Dean for the Natural Sciences

 

    School of Humanities and Sciences

Research Interests:
Algebraic and Geometric topology



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Eliashberg, Yakov
Herald L. and Caroline L. Ritch Professor of Mathematics
383-S

Yakov Eliashberg

Herald L. and Caroline L. Ritch Professor of Mathematics
Stanford University
Mathematics

Office: 383-S

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

Phone: (650) 723-4073
Email:
Research Interests Symplectic Geometry Topology Several Complex Variables

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Søren Galatius

Professor
Stanford University
Mathematics

Office: 383-DD

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

Phone: (650) 723-2969
Email:
Website: http://math.stanford.edu/~galatius/

Research Interests:
Algebraic topology



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Kerckhoff, Steven
Robert Grimmett Professor in Mathematics
383-G

Steven Kerckhoff

Robert Grimmett Professor in Mathematics
Stanford University
Mathematics

Office: 383-G

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

Phone: (650) 723-4665
Email:
Research Interests: Hyperbolic structures Teichmüller Space

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Maryam Mirzakhani

Professor
Stanford University
Mathematics

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

Phone: (650) 723-3259
Email:
Research Interests: Teichmüller Theory Ergodic Theory

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Perlmutter, Nathan
Postdoctoral Scholar
384-D

Nathan Perlmutter

Postdoctoral Scholar
Stanford University
Mathematics

Office: 384-D

Address:
450 Serra Mall
Building 380
Stanford, CA 94305

Phone: (650) 736-6996
Email:

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