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Topology, Geometry and Physics: The Witten Conjecture

Who: Gregory M. Naber, Cal State-Chico (and Saint Joseph's University)

When and Where: Thursday, February 26, in Barbelin 226 at 11:50.

Food? Yes, sandwiches, chips, and soda. Food will be available prior to the start of the colloquium in BL 226 beginning at 11:30. Anyone attending the talk is welcome.

Audience: Math and CS faculty and students and others interested in mathematical physics and topology.

Abstract: The Donaldson invariants of a smooth 4-manifold M are subtle probes into the differential topological structure of M. They are defined in terms of the structure of a moduli space of solutions to certain partial differential equations proposed by physicists (Yang-Mills) to model the interactions between elementary particles. Ed Witten found that they can also be viewed as expectation values for certain observables in a Topological Quantum Field Theory. His insight into the physics of this TQFT led him to conjecture that the information contained in the Donaldson invariants can also be retrieved from a much simpler set of equations (Seiberg-Witten). The impact of the conjecture, especially on topology, has been spectacular. The rather modest objective of this lecture is to provide the background necessary to understand what the conjecture says.

Gregory L. Naber is a visiting member of the SJU Mathematics and Computer Science Department. He is a member of the math department at Cal State-Chico and is the author of several books on topology.

Presented by the SJU Math and Computer Science Department.

Sean Forman and Jonathan Hodgson, colloquium committee