Contraction algebras, plumbings and flops

Abstract: I will explain how certain symmetric Nakayama algebras (under the disguise of "contraction algebras") control and prove theorems about geometric objects on both sides of mirror symmetry. As part of this, I will explain our symplectic geometry model, our algebraic geometry model, and then how the contraction algebra relates them. The cohomology of objects in the underlying categories are naturally modules for the associated contraction algebra, and I will explain how to use this information to obtain otherwise tricky results, such as a classification of spherical (and more generally, fat-spherical) objects. This has purely topological corollaries. One feature, which I will probably gloss over but is actually fundamental, is that our categories have a dependence on the characteristic of the ground field. This is joint work with Ivan Smith (arXiv:2010.10114).

mathematical physicscommutative algebraalgebraic geometryrings and algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

( paper | slides | video )

Comments: Thursday 29th October 2020, 12:00 – 13:00 (GMT) us02web.zoom.us/j/89958893469?pwd=aWFWQXZnMXczUFdJc282bWx3bE5Idz09 Meeting ID: 899 5889 3469 Passcode: Lagoon

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Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)

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