Date/Time
Date(s) - 14/11/2025
3:30 pm - 4:30 pm

Location: Hamilton Hall, Room 305

Speaker: Mike Roth (Queen’s University)

Title: Seshadri constants on P^1 x P^1 and applications to the symplectic packing problem.

Abstract:
Given a manifold M with a symplectic form, the Gromov width of M is the radius of the largest ball which can be symplectically embedded into M. More generally, fixing a positive integer r, one can look at the largest radius so that r disjoint balls of that radius can be symplectically embedded in M. If M has finite volume an equivalent formulation is to ask which proportion of the volume of M can be taken up by r disjoint symplectic balls. Either of these versions are known as the symplectic packing problem.

There are very few symplectic manifolds for which these numbers are known.  In this talk we will give the solution when M is the product of P^1 with itself. The solution uses an equivalence, developed in the 1990’s by McDuff, Polterovich, and Biran, between this problem and the algebro-geometric problem of computing the “r-point Seshadri constant’’.

The main point of the talk is to explain the problem, the answer on P^1 x P^1, and some parts of the equivalence above. One surprising part of the answer is the dichotomy between the cases that r is even or odd. This is joint work with Chris Dionne.

Coffee will be served in HH 216 at 3:00pm. All are welcome.