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Associative Yang-Baxter equation and related 1-CY categories

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Alexander Polishchuk (Oregon) - Seminar Algebraic Geometry (SAG)

What
  • Seminar
When Oct 12, 2017
from 10:30 am to 11:30 am
Where Bonn, Hörsaal MPI, Vivatsgasse 7, 53111 Bonn
Contact Name Sachinidis
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The talk is based on the joint work with Yanki Lekili. The associative Yang-Baxter equation
is a quadratic equation related to both classical and quantum Yang-Baxter equations. It appears
naturally in connection with triple Massey products in the derived category of coherent sheaves
on elliptic curve and its degenerations. We show that all of its nondegenerate trigonometric solutions
are obtained from Fukaya categories of some noncompact surfaces. We use this to prove that
any two simple vector bundles on a cycle of projective lines are related by a sequence
of spherical twists.