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





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.





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





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