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 here until his retirement in 2006. The accomplishments of Allan Hatcher, who was at UCLA from 1976 until 1984, include the proof of the Smale Conjecture (published in 1983).
More than 60 students, supervised by eleven advisors, have received Ph. D. degrees from UCLA for dissertations on topological subjects.
We run a weekly in-house Topology Seminar, on Wednesdays and/or Fridays at 3pm. 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.
For more information about the Topology group, please consult their website.