Mathematical Physics

Gauge Theory and Khovanov Homology

Speaker: 
Edward Witten
Date: 
Fri, Feb 17, 2012
Location: 
PIMS, University of Washington
Abstract: 
After reviewing ordinary finite-dimensional Morse theory, I will explain how Morse generalized Morse theory to loop spaces, and how Floer generalized it to gauge theory on a three-manifold. Then I will describe an analog of Floer cohomology with the gauge group taken to be a complex Lie group (rather than a compact group as assumed by Floer), and how this is expected to be related to the Jones polynomial of knots and Khovanov homology.

A Functional Integral Representation for Many Boson Systems

Speaker: 
Joel Feldman
Date: 
Fri, Oct 5, 2007
Location: 
University of British Columbia, Vancouver, Canada
Conference: 
CRM-Fields-PIMS Prize Lecture
Abstract: 
This is the 2007 CRM-Fields-PIMS prize lecture by Joel Feldman, with citation by David Brydges.

Introduction to Marsden & Symmetry

Speaker: 
Alan Weinstein
Date: 
Wed, Jul 20, 2011
Location: 
Vancouver Convention Center, BC, Canada
Conference: 
ICIAM 2011
Abstract: 
Alan Weinstein is a Professor of the Graduate School in the Department of Mathematics at the University of California, Berkeley. He was a colleague of Jerry Marsden throughout Jerry’s career at Berkeley, and their joint papers on “Reduction of symplectic manifolds with symmetry” and “The Hamiltonian structure of the Maxwell-Vlasov equations” were fundamental contributions to geometric mechanics.

Self-Interacting Walk and Functional Integration

Author: 
David Brydges
Date: 
Thu, Sep 14, 2000
Location: 
University of British Columbia, Vancouver, Canada
Conference: 
PIMS Distinguished Chair Lectures
Abstract: 

These lectures are directed at analysts who are interested in learning some of the standard tools of theoretical physics, including functional integrals, the Feynman expansion, supersymmetry and the Renormalization Group. These lectures are centered on the problem of determining the asymptotics of the end-to-end distance of a self-avoiding walk on a TeX Embedding failed!-dimensional simple cubic lattice as the number of steps grows. When TeX Embedding failed! the end-to-end distance has been conjectured to grow as Const. TeX Embedding failed! where TeX Embedding failed! is the number of steps. We include a theorem, obtained in joint work with John Imbrie, that validates the TeX Embedding failed! conjecture in the simplified setting known as the ``Hierarchial Lattice.''

Notes: 
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