A gluing construction for Ginzburg algebras of triangulated surfaces

Abstract: Ginzburg algebras associated to triangulated surfaces are a class of 3-Calabi-Yau dg-algebras which categorify the cluster algebras of the underlying marked surfaces. In this talk, we will discuss a description of these Ginzburg algebras in terms of the global sections of a constructible cosheaf of dg-categories (modelling a perverse Schober). This cosheaf description shows that the Ginzburg algebras arise via the gluing of relative versions of Ginzburg algebras associated to the faces of the triangulation along their common edges. The definition of the cosheaf is inspired by a result of Ivan Smith, by which the finite derived category of such a Ginzburg algebra embeds into the Fukaya category of a Calabi-Yau 3-fold equipped with a Lefschetz fibration to the surface.

mathematical physicscommutative algebraalgebraic geometryrings and algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

( slides | video )

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Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)

Series comments: Description: Research webinar series

The LAGOON webinar series was supported as part of the International Centre for Mathematical Sciences (ICMS) and the Isaac Newton Institute for Mathematical Sciences (INI) Online Mathematical Sciences Seminars and is now sponsored by the University of Cologne and the University of Pavia. Please register here to obtain the Zoom link and password for the meetings.

LAGOON will take place online every last Wednesday of the month from 14:00-15:00 (Time Zone Berlin, Rome, Paris).

Videos of the talks can be viewed here.

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