Multiplicative preprojective algebras in geometry and topology

Abstract: In 2006, Crawley-Boevey and Shaw defined the multiplicative preprojective algebra (MPA) to study certain character varieties. More recently, MPAs appeared in work of Etgü--Lekili in the study of Fukaya categories of 4-manifolds. Nice properties of the (additive) preprojective algebra are expected to hold for MPAs, but most proof techniques are not available. In joint work with Travis Schedler, we define the strong free product property, following older work of Anick. Using this property, we prove MPAs are 2-Calabi--Yau algebras for quivers containing a cycle. Moreover, using a result of Bocklandt--Galluzzi--Vaccarino, we prove the formal local structure of multiplicative quiver varieties is isomorphic to that of a (usual) quiver variety. In this talk, I'll survey these ideas and illustrate them in small examples.

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.

Video recordings of past talks until April 2022 can still be viewed on the ICMS webpage here.

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