Wednesday, February 21, 2018
1:30 pm
Lauritsen 469

Physics and Geometry Seminar

Geometric Recursion
Jorgen Andersen, Aarhus University

Geometric Recursion is a very general machinery for constructing mapping class group invariants objects associated to two dimensional surfaces. After presenting the general abstract definition we shall see how a number of constructions in low dimensional geometry and topology fits into this setting. These will include the Mirzakhani-McShane identies, mapping class group invariant closed forms on Teichm├╝ller space (including the Weil-Petterson symplectic form) and the Goldman symplectic form on moduli spaces of flat connections for general compact simple Lie groups. If time permits we shall see how Geometric Recursion provides us a with a kind of categorification of Topological Recursion, namely any application of Topological Recursion can be lifted to a Geometric Recursion setting involving continuous functions on Teichm├╝ller space, where the connection back to Topological Recursion is obtained by integration over the moduli space of curve. The work presented is joint with G. Borot and N. Orantin.

Contact Carol Silberstein carol@theory.caltech.edu
For more information see http://theory.caltech.edu/mathphy/
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