#### Algebra & Combinatorics Seminar

##### Venue: LH-1, Mathematics Department

To any convex integral polygon $N$ is associated a cluster integrable system that arises from the dimer model on certain bipartite graphs on a torus. The large scale statistical mechanical properties of the dimer model are largely determined by an algebraic curve, the spectral curve $C$ of its Kasteleyn operator $K(x,y)$. The vanishing locus of the determinant of $K(x,y)$ defines the curve $C$ and coker $K(x,y)$ defines a line bundle on $C$. We show that this spectral data provides a birational isomorphism of the dimer integrable system with the Beauville integrable system related to the toric surface constructed from $N$.

This is joint work with Alexander Goncharov and Richard Kenyon.

Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ;     E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 06 Mar 2020