The classification of 3-fold flops via Jacobi algebras

Abstract: The talk will give an overview of the analytic classification of smooth, simple, 3-fold flops. There are three main aspects: (1) reducing the problem to the classification of certain noncommutative finite dimensional algebras, (2) a full understanding of those algebras, then lastly (3) building the associated geometry for each algebra in that class. There are various bonus corollaries. The talk will be algebraic, and so will focus mostly on (1) and (2), where new techniques in A∞ algebras and in noncommutative standard bases will be explained. Perhaps the main point is that a new invariant of Jacobi algebras on the two-loop quiver called the "algebraic length" will be introduced, and I will speculate on how general this construction really is. Part (1) is joint with Joe Karmazyn and Emma Lepri, the rest is joint with Gavin Brown.

mathematical physicscommutative algebraalgebraic geometryrings and algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

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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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