Time and place: 16:00 Friday 6 May in Weatherburn LT
Speaker: Norman Do (Monash University)
Title: Counting curves on surfaces
Abstract: Choose an even number of points on the boundary of a surface. How many ways are there to pair up these points with disjoint arcs on the surface? The most basic instance of this problem produces the Catalan numbers while the problem in general exhibits a surprisingly rich structure. For example, we will show that this enumeration obeys an effective recursion and exhibits polynomial behaviour. Moreover, there are unexpected connections to algebraic geometry and mathematical physics.
Speaker: Norman Do (Monash University)
Title: Counting curves on surfaces
Abstract: Choose an even number of points on the boundary of a surface. How many ways are there to pair up these points with disjoint arcs on the surface? The most basic instance of this problem produces the Catalan numbers while the problem in general exhibits a surprisingly rich structure. For example, we will show that this enumeration obeys an effective recursion and exhibits polynomial behaviour. Moreover, there are unexpected connections to algebraic geometry and mathematical physics.