Derived equivalences from mutations of ice quivers with potential

Abstract: In 2009, Keller and Yang categorified quiver mutation by interpreting it in terms of equivalences between derived categories. Their approach was based on Ginzburg’s Calabi--Yau algebras and on Derksen--Weyman--Zelevinsky’s mutation of quivers with potential. Recently, Matthew Pressland has generalized mutation of quivers with potential to that of ice quivers with potential. We will explain how his rule yields derived equivalences between the associated relative Ginzburg algebras, which are special cases of Yeung’s deformed relative Calabi–Yau completions arising in the theory of relative Calabi--Yau structures due to Toën and Brav--Dyckerhoff. We will illustrate our results on examples arising in the work of Baur--King--Marsh on dimer models and cluster categories of Grassmannians. If time permits, we will also sketch a categorification of mutation at frozen vertices as it appears in recent work of Fraser--Sherman-Bennett on positroid cluster structures.

mathematical physicscommutative algebraalgebraic geometryrings and algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

Comments: Meeting Link Thursday, 12:00 - 13:00 (BST, UK Time) us02web.zoom.us/j/87160036709?pwd=aGtBdkx4VDFuY0l2UlkzRFdiYUF3dz09 Meeting ID: 871 6003 6709 Passcode: LAGOON

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Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)

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