Combinatorics of Surface Deformations

02/22/2011 - 12:15pm
02/22/2011 - 1:10pm
Satyan Devadoss (Williams College)

We consider the moduli space of surfaces with boundary and marked points. Such spaces appear in algebraic geometry and topology, playing a strong role in holomorphic curves, open-closed string theory, and quantum cohomology. We consider a combinatorial framework to view the compactification of this space based on the pair-of-pants decomposition of the surface. This leads to a classification of all such spaces which can be realized as polytopes, capturing an elegant hidden algebraic structure.

Millikan 208 (Pomona College)