Program
Topological field theory in two dimensions, modular operads, and homotopy theory
Student No.:50
Time:【Updated】Mon/Wed 13:30-15:05, 2017-06-26~2017-07-19
Instructor:Ezra Getzler  [Northwestern University]
Place:Conference Room 3, floor 2, Jin Chuan Yuan West Building
Starting Date:2017-6-26
Ending Date:2017-7-19

 

 

Description:

 

We start by using hyperbolic geometry to construct moduli spaces of Riemann surfaces. Compactifying these moduli spaces, we obtain a definition of topological field theory in two dimensions. Studying the homotopy theory of these moduli spaces yields a lot of information about the structure of topological field theories: for illustration, we will explain the proofs of the famous theorem of Moore and Seiberg.

 

In the second part of the course, we will discuss a real version of all of this: a real Riemann surface is a Riemann surface with an orientation reversing involution. This leads to the definition of open/closed and unoriented topological field theories. We discuss the generalization to this setting of the theorem of Moore and Seiberg, and also Costello’s famous theorem.

 

 

Prerequisite:

 

Manifolds, simplicial complexes, homotopy groups, singular homology and cohomology, de Rham cohomology

 

 

Reference:

 

Geometry and spectra of compact Riemann surfaces, Peter Buser, Modern Birkhäuser Classics

 

Natural triangulations associated to a surface, B.H.Bowditch and D.B.A.Epstein, Topology 27, 91-117

 

Lectures on tensor categories and modular functors, Bojko Bakalov and Alexander Kirillov, University Lecture Series 21, AMS

 

Topological conformal field theories and Calabi-Yau categories, Kevin Costello, Advances in Mathematics 210, 165-214