Topology Seminar, Chris Arretines (CUNY): 'Combinatorial and algorithmic questions in low dimensional topology'

Wednesday, April 22, 2015
4:15 PM - 5:30 PM (ET)
ESC 638
Event Type
David Constantine,

Abstract: I will discuss how several geometric and topological questions related to curves on surfaces can be presented in terms of combinatorial data, and I will outline algorithmic methods for answering these questions. In particular, I will discuss how to determine intersection numbers for collections of curves, and how to determine whether or not a collection of curves is filling, which means that the complement of the curves is a disjoint union of topological disks. The study of these properties is motivated in part by the role of curves on surfaces in proving several powerful theorems related to Teichmueller space, which I will try to convey. Time permitting, I will also showcase some interesting constructions motivated by exploring the above algorithms.

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