Combinatorics of surface deformations


Stayan Devadoss

14:00:00 - 15:00:00
103 , Mathematics Research Center Building (ori. New Math. Bldg.)

In the 1970s, Deligne and Mumford constructed a way to keep track of particle collisions using Geometric Invariant Theory. Later, Kontsevich and Fukaya generalized these ideas when studying deformation quantization to include surfaces with boundary and marked points. We consider a simple, combinatorial framework to view these spaces based on the pair-of-pants decomposition of surfaces. This leads to a classification of all such spaces which can be realized as convex polytopes, capturing elegant hidden algebraic structures.