Topology, Algebraic Geometry, and Dynamics Seminar (TADS): The compactness problem in generalized Seiberg-Witten theory

Speaker:  Boyu Zhang, University of Maryland

Title:  The compactness problem in generalized Seiberg-Witten theory

Abstract:  The Seiberg-Witten equation is a system of partial differential equations defined on fiber bundles.  Since its introduction in the 90s, Seiberg-Witten theory has yielded numerous significant results in low-dimensional topology.  I will talk about a generalization of the Seiberg-Witten equation on 3-manifolds, and discuss the compactness problem for the moduli space of its solutions.  This problem was first proposed and studied by Taubes in 2013.  I will discuss some of the recent progress in this field, and present a result that compares the compactification of moduli spaces from algebraic geometry (by Morgan-Shalen) and from analysis (by Taubes) via harmonic maps to R-trees.  This talk is based on joint works with Siqi He, Thomas Walpuski, and Richard Wentworth.

Time:  Friday, September 20, 1:30pm – 2:30pm

Place:  Exploratory Hall, room 4208