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

### Gunnar Carlsson

Professor EmeritusStanford University

Mathematics

**Office:**382-M

**Address:**

450 Serra Mall

Building 380

Stanford, CA 94305-2125

**Phone:**(650) 723-2224

**Email:**gunnar@math.stanford.edu

**Website:**http://math.stanford.edu/~gunnar/

**Research Interests:**algebraic topology; algebraic K-theory; number theory

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### Tom Church

Assistant ProfessorStanford University

Mathematics

**Office:**383-Y

**Address:**

450 Serra Mall

Building 380

Stanford, CA 94305-2125

**Phone:**(650) 725-8572

**Email:**church@math.stanford.edu

**Website:**http://math.stanford.edu/~church/

**Research Interests:**topology, especially low-dimensional topology

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Professor Emeritus Barbara Kimball Browning Professor in the School of Humanities and Sciences

### Ralph Cohen

Professor Emeritus Barbara Kimball Browning Professor in the School of Humanities and SciencesStanford University

Mathematics

**Office:**383-X

**Address:**

450 Serra Mall

Building 380

Stanford, CA 94305-2125

**Phone:**(650) 723-1862

**Email:**ralph@math.stanford.edu

**Website:**http://math.stanford.edu/~ralph/

**Awards:**Bass University Fellow in Undergraduate Education; Senior Associate Dean for the Natural Sciences, School of Humanities and Sciences

**Research Interests:**algebraic and geometric topology

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Herald L. and Caroline L. Ritch Professor of Mathematics

### Yakov Eliashberg

Herald L. and Caroline L. Ritch Professor of MathematicsStanford University

Mathematics

**Office:**383-S

**Address:**

450 Serra Mall

Building 380

Stanford, CA 94305-2125

**Phone:**(650) 723-4073

**Email:**eliash@math.stanford.edu

**Research Interests**symplectic geometry; topology; several complex variables

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### Steven Kerckhoff

Robert Grimmett Professor in MathematicsStanford University

Mathematics

**Office:**383-G

**Address:**

450 Serra Mall

Building 380

Stanford, CA 94305-2125

**Phone:**(650) 723-4665

**Email:**spk@math.stanford.edu

**Research Interests:**hyperbolic structures; Teichmüller space

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