Deformation theory of Cohomological Field Theories

Abstract: In this talk, I will develop the deformation theory of Cohomological Field Theories (CohFTs), that is algebras over the moduli spaces of stable curves with marked points. This will lead to two new natural extensions of the notion of a CohFT: homotopical (necessary to structure chain-level Gromov--Witten invariants) and quantum (with examples found in the works of Buryak--Rossi on integrable systems). I will introduce a new version of Kontsevich's graph complex, enriched with tautological classes, and I will use it to study a new universal deformation group which acts naturally on the moduli spaces of quantum homotopy CohFTs. This group is shown to contain both the prounipotent Grothendieck--Teichmüller group and the Givental group. (Joint work with Vladimir Dotsenko, Sergey Shadrin, Arkady Vaintrob available at arxiv.org/abs/2006.01649.)

mathematical physicscommutative algebraalgebraic geometryrings and algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

( paper | slides )

Comments: Zoom link: icms-org-uk.zoom.us/j/81601767022?pwd=dDZwV1dEeW1STUZkOTUwTlNiVmZodz09 Meeting ID: 816 0176 7022 Passcode: LAGOON

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Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)

Series comments: Description: Research webinar series

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