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.


  (650) 723-1927
  Building 380, 382-M
  (650) 723-2224
  Building 380, 382-M
Professor Emeritus Barbara Kimball Browning Professor in the School of Humanities and Sciences
  (650) 723-1862
  Building 380, 383-X
Herald L. and Caroline L. Ritch Professor of Mathematics
  (650) 723-4073
  Building 380, 383-S
Robert Grimmett Professor in Mathematics, Emeritus
  (650) 723-4665
  Building 380, 383-G
  Building 380, 383-X
Szegö Assistant Professor
  Building 380, 382-B