UCLA Topology Group

People History Seminars Links


Faculty:
 Research interests
Robert Brown Algebraic Topology, Fixed point theory
Ciprian Manolescu Gauge theory, Symplectic geometry, Low-dimensional topology
Geoffrey Mess Low-dimensional topology


Postdocs:
Tova Brown Bordered Heegaard Floer homology
Allison Gilmore Knot homology theories, 3-manifold topology
Liam Watson Low-dimensional topology, Khovanov homology


Emeritus: Regular visitors:
Robert Edwards Ian Ferris
  Dan Gottlieb
Graduate students: Kevin Iga
Tye Lidman Phil Martens
Yajing Liu  
Chris Scaduto  


Faculty in related fields: Paul Balmer, Kefeng Liu, Gang Liu, Christian Haesemeyer, Igor Pak, Peter Petersen, Raphael Rouquier.

History:

Topological research at UCLA began with the arrival of Robert Sorgenfrey in 1942, soon after he earned a Ph. D. at the University of Texas under the legendary topologist R. L. Moore. High points in the research accomplishments of topologists at UCLA include the solution by Robion Kirby, who was at UCLA from 1965 to 1971, (with Laurence Siebenmann) of four of the seven problems listed by John Milnor in 1963 as the most important in topology at that time. Kirby first presented his famous "torus trick", the key to the solutions, in a UCLA seminar in the summer of 1968. Another of the Milnor problems, the Double Suspension Conjecture was solved by Robert Edwards, who came to UCLA in 1970 and remained until his retirement in 2006. The accomplishments of Allan Hatcher, who was at UCLA from 1976 until 1984, include the proof, published in 1983, of the Smale Conjecture.

About 60 students, supervised by nine advisors, have received Ph. D. degrees from UCLA for dissertations on topological subjects.

Seminars:

We run a weekly in-house Topology Seminar, on Wednesdays at 3pm (or 1pm during the summer). We typically choose a topic each quarter, and the group members take turns in giving lectures about that subject. Recent topics have included: the Casson invariant; Khovanov homology; Khovanov-Rozansky homology; combinatorial Heegaard Floer homology via grid diagrams; rational homotopy theory; intersection cohomology; Reshetikhin-Turaev-Witten invariants.

In addition, we have a monthly Joint UCLA / USC / Caltech Topology Seminar, where we invite outside speakers to talk about current research developments.

Other seminars of interest:

  • UCLA Geometry Seminar

  • USC Geometry / Topology Seminars

  • Caltech Geometry and Topology Seminar


    Links:

  • Topology (on Wikipedia)
  • Low dimensional topology (on Wikipedia)
  • Knot Atlas
  • Table of Knot Invariants
    		•  Videos:

  • Sphere eversion
  • Not Knot (Part I)
  • Not Knot (Part II)
    		•