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
Friday, February 1, 2019 at 4:30 pm
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