Stanford University
Topology Seminar 2002-3 Unless otherwise noted, all seminars are
on |

**Fall 2002 Schedule**** **

October 1, 2002

**Speaker**: Constantin Teleman, Cambridge University

**Title**:** **Twisted K theory and the moduli of G-bundles over
a Riemann surface

**Abstract**: We
explain in this talk how the K-theoretic "intersection pairings" on
the moduli of G-bundles over compact Riemann surface are controlled by
defortmations of the Verlindealgebra, generalizing well-known results about
powers of the determinant bundle. The moral justification of this fact is based
on the theorem of Freed, Hopkins and the speaker, that the Verlinde algebra of
G is expressible as a twisted K-theory of G, equivariant for its own
conjugation action. The twistings in that theorem are multiples of the
determinanttwisting of BU; the use of higher twistings allows one to
incorporate other vector bundles on the moduli space.

October 8

**Title:
Abstract **

October 15, 2002

**Title: **

**Abstract:**

October 22, 2002

**Speaker**: Gunnar Carlsson, Stanford University

**Title: **Algebraic Topology and Feature
Detection

**Abstract:** We are interested in locating various kinds of
"features" of a geometric object, such as corners. edges, cone
points, etc., when we are given the geometric object via a sampled "point
cloud" from it. I will
describe various homological criteria which can be used as heuristics in
finding these features.