Brown University

Mathematics Department Colloquium

Fridays – 4:30PM – Barus-Holley 190

March 17

Rick Kenyon, UBC and Brown

Dimers, the complex Burgers equation, and inscribing rational curves in polygons

Abstract: This is joint work with Andrei Okounkov. Given a polygon P with 3n sides, when can you find a degree-n rational curve inscribed in P? We answer this question for the family of polygons having sides with slopes 0,1,infinity. This result arose from a completely different area, studying the so-called dimer model of statistical mechanics. We'll show the connection and give a sketch of the proof.