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UNIVERSITY OF CALIFORNIA, SANTA BARBARA BERKELEY DAVIS IRVINE LOS ANGELES MERCED RIVERSIDE SAN DIEGO SAN FRANCISCO
 

Summary: UNIVERSITY OF CALIFORNIA, SANTA BARBARA
BERKELEY ˇ DAVIS ˇ IRVINE ˇ LOS ANGELES ˇ MERCED ˇ RIVERSIDE ˇ SAN DIEGO ˇ SAN FRANCISCO
CSANTA BARBARA ˇ SANTA CRUZ
Geometry, Topology, and Physics Seminar
Introduction to Wall-Crossing Formulas
David Morrison
UCSB
Friday, October 3rd, 2008, 4:00 p.m.
Room 6635 South Hall
Abstract: Wall-crossing formulas first arose in the celebrated work of Seiberg &
Witten, where they related the count of "BPS quantum states" in one part of the
moduli space (of certain quantum field theories) to the count in another part of the
moduli space: this led directly to a new method for computing Donaldson invariants
of 4-manifolds, and the rest is history.
We will introduce this area of study, aiming at the dramatic recent progress in
understanding this kind of formula in other contexts, including cases where the curves
on a Calabi­Yau manifold are being counted. The ingredients for this progress include
considerations of symplectic geometry and a study of "Stokes factors" in differential
equations. There is also a beautiful physics argument for the wall-crossing formulas
(in some cases), involving a study of the 4-dimensional physical theory on R3

  

Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara

 

Collections: Mathematics