University of Durham
Low-dimensional topology has seen a proliferation of new invariants and techniques over the last decade or so which are intimately interrelated. The ideas behind them are approachable from a number of points of view: for example from algebraic geometry, differential geometry, algebraic topology, or from representation theory. The invariants include Khovanov homology and related constructions, Floer homologies, and various gauge theories.
The course aims to present a broad selection of these ideas, covering the construction, the properties, and applications.
The three main lecture course topics are:
· Heegaard-Floer homology (Matthew Hedden, Michigan State University)
· Khovanov homology and its offspring. (Jacob Rasmussen, Cambridge)
· Contact 3-manifolds and holomorphic curves. (Chris Wendl, UCL)
These lecture courses will be supplemented by tutorial sessions.