Mike Roth (Queen's University)
Title: r-point Seshadri constants and the solution to the symplectic听packing problem for P^1 x P^1
Abstract: The symplectic packing problem asks how much of the volume of a symplectic manifold M can be filled by r disjoint symplectic balls of the same dimension as M.
If, asymptotically, one can fill all of the volume one says that there is a full packing. If not, one says that there is a packing obstruction.
The symplectic packing problem was introduced by McDuff and Polterovich,
following work of Gromov. If the symplectic manifold is the real
4-manifold underlying a complex algebraic surface, then results of McDuff and Polterovich, and Biran connect the symplectic packing problem with algebraic geometry on that surface. This talk will discuss the complete solution to the symplectic packing problem on P^1 x P^1, using this connection.
On P^1 x P^1 there is more than one choice of symplectic form, and an interesting feature of the solution is that the answer varies with the form and shows a surprising dependence on the parity of r.
This is joint work with Chris Dionne.
Location: In person at UQAM PK-5675 (Zoom available upon request)
The organizers (Joel Kamnitzer, Jake Levinson, Steven Lu and Brent Pym)
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