From symplectic geometry to combinatorics and back
From symplectic geometry to combinatorics and back
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Dan Cristofaro-Gardiner , Harvard University
A much studied combinatorial object associated to a polytope is its "Ehrhart function". 听This is typically studied for integral or rational polytopes. 听The first part of the talk will be about joint work with Li and Stanley extending this theory to certain irrational polytopes; the idea for this was inspired by work of McDuff and Schlenk on symplectic embeddings of four-dimensional ellipsoids. 听In the second part of the talk, I will introduce recent joint work with Holm, Mandini, and Pires, which aims to apply this "irrational" Ehrhart theory to study embeddings of ellipsoids into four-dimensional symplectic toric manifolds. 听