Date/Time:19 Sep 2018 15:00

Venue: S17 #05-11 SR5

Speaker: Daniel Mathews, Monash University

**Counting curves on surfaces**

Consider the following elementary combinatorial problem in low-dimensional topology: Fix a surface S and a finite set F of points on its boundary. How many configurations of disjoint curves are there on S whose boundary is F?

Venue: S17 #05-11 SR5

Speaker: Daniel Mathews, Monash University

Consider the following elementary combinatorial problem in low-dimensional topology: Fix a surface S and a finite set F of points on its boundary. How many configurations of disjoint curves are there on S whose boundary is F?

In the simplest case this problem gives the Catalan numbers, and in general we find the problem has a rich structure, involving notions from topological recursion, moduli spaces, and quantum mechanics.

We will discuss some aspects of this problem, and related questions, including joint work with Norman Do, Jian He, and Musashi Koyama.

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