**Special Seminar**

Come join us **Friday, February 1, 2019 at 4:30 pm in RM 507, Professor ****Anton Zeitlin** (Louisiana State University) will be giving a special lecture about **“Super-Teichmüller Spaces, Spin Structures, Penner Coordinates, and Applications”.**

**Abstract**

The Teichmüller space, which parametrizes Riemann surfaces, is a

fundamental space that is important in many areas of mathematics and physics.

Recently, generalizations of this space have been intensely studied. Examples of

such higher Teichmüller spaces are the so-called super-Teichmüller

spaces. They appear in the application of the combinatorial approach to spin

structures on Riemann surfaces and generalizations to supermanifolds. The

super-Teichmüller spaces naturally arise as higher Teichmüller spaces,

corresponding to supergroups that play an important role in geometric

topology, algebraic geometry, and mathematical physics.

In this talk, I will give a solution of the long-standing problem

of describing an analogue of Penner coordinates on super-Teichmüller

spaces and their generalizations. The importance of these coordinates is

justified by two remarkable properties: the action of the mapping class

group is rational and the Weil-Petersson form is given by a simple explicit

formula.

I will end my presentation with a description of some of the emerging

applications of this theory.

**Mathematics Hall, Room 507**

**Fri****day, February 1, 2019 at 4:30 pm**