BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Harold Williams (USC) DTSTART:20201016T220000Z DTEND:20201016T230000Z DTSTAMP:20260423T005748Z UID:caltechGT/3 DESCRIPTION:Title: Kasteleyn operators from mirror symmetry\nby Harold Williams (USC) a s part of Caltech geometry/topology seminar\n\n\nAbstract\nIn this talk we explain an interpretation of the Kasteleyn operator of a doubly-periodic bipartite graph from the perspective of homological mirror symmetry. Speci fically\, given a consistent bipartite graph G in T^2 with a complex-value d edge weighting E we show the following two constructions are the same. T he first is to form the Kasteleyn operator of (G\,E) and pass to its spect ral transform\, a coherent sheaf supported on a spectral curve in (C*)^2. The second is to take a certain Lagrangian surface L in T^* T^2 canonicall y associated to G\, equip it with a brane structure prescribed by E\, and pass to its homologically mirror coherent sheaf. This lives on a toric com pactification of (C*)^2 determined by the Legendrian link which lifts the zig-zag paths of G (and to which the noncompact Lagrangian L is asymptotic ). As a corollary\, we obtain a complementary geometric perspective on cer tain features of algebraic integrable systems associated to lattice polygo ns\, studied for example by Goncharov-Kenyon and Fock-Marshakov. This is j oint work with David Treumann and Eric Zaslow.\n LOCATION:https://researchseminars.org/talk/caltechGT/3/ END:VEVENT END:VCALENDAR