Topology

Gauge Theory and Khovanov Homology

Speaker: 
Edward Witten
Date: 
Sat, Feb 18, 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.

Class: 
Scientific
Subject: 
Mathematics
Differential Geometry and Geometric Analysis
Topology
Physics
Mathematical Physics
Particle Physics and Quantum Field Theory

Hyperplane Arrangements and Applications

Some photos from the Hyperplane Arrangements and Applications conference which took place at UBC Vancouver, August 8-12. This conference was held in honour of Hiroaki Terao.

Conference: 
Hyperplane Arrangements and Applications
Date: 
Mon, Aug 8, 2011
Class: 
Scientific
Subject: 
Algebraic Geometry
Combinatorics
Algebra
Topology

Modelling Aperiodic Solids: Concepts and Properties of Tilings and their Physical Interpretation

Author: 
Franz Gaehler
Date: 
Thu, Aug 1, 2002
Location: 
University of Victoria, Victoria, Canada
Conference: 
Aperiodic Order, Dynamical Systems, Operator Algebras and Topology
Abstract: 

Topics: Quasicrystals, Quasiperiodicity, Translation module, Repetitivity, Local Isomorphism, Mutual Local Derivability, Matching Rules, Covering Rules, Maximal Coverings

Notes: 
PDF icon Gaehler_Franz_2.pdf
Class: 
Scientific
Subject: 
Condensed Matter and Statistical Mechanics
Topology

Cohomology of Quasiperiodic Tilings

Author: 
Franz Gaehler
Date: 
Thu, Aug 1, 2002
Location: 
University of Victoria, Victoria, Canada
Conference: 
Aperiodic Order, Dynamical Systems, Operator Algebras and Topology
Abstract: 

Topics:

• Quasiperiodic tilings

• The hull of a tiling

• Approximation the hull by CW-spaces

• Application to canonical projection tilings

• Relation to matching rules

• Towards an interpretation

Notes: 
PDF icon Gaehler_Franz_1.pdf
Class: 
Scientific
Subject: 
Discrete Mathematics
Topology

Torsion invariants of 3-manifolds

Author: 
Vladimir Turayev
Date: 
Mon, Jan 20, 2003
Location: 
University of Calgary, Calgary, Canada
Conference: 
PIMS Distinguished Chair Lectures
Abstract: 

This series of six lectures is intended for a general audience. The aim of the lectures is to survey the theory of torsions of 3-dimensional manifolds. The torsions were introduced by Kurt Reidemeister in 1935 to give a topological classification of lens spaces. Recent interest in torsions is due to their connections with the Seiberg-Witten invariants of 4-manifolds and the Floer-type homology of 3-manifolds. The lectures will cover the above topics.

Notes: 
PDF icon Turaev.pdf
Class: 
Scientific
Subject: 
Topology

Pages