Where are the complex curves in Khovanov homology?

Abstract: Since the advent of gauge theory, many modern tools exhibit a close connection with complex curves and a heightened sensitivity to objects from the complex realm. Surprisingly, this is true even for Khovanov homology, whose construction is combinatorial rather than geometric. I will discuss this in the context of joint work with Isaac Sundberg that uses Khovanov homology to study knotted surfaces in 4-space, especially (compact pieces of) complex curves in the 4-ball.

algebraic geometryanalysis of PDEsalgebraic topologycomplex variablesdifferential geometrygeneral topologygeometric topologyK-theory and homologymetric geometrysymplectic geometry

Audience: researchers in the topic

CRM - Séminaire du CIRGET / Géométrie et Topologie

Series comments: Hybrid seminar of geometry and topology. Laboratory : CIRGET - www.cirget.uqam.ca The homepage of the seminar is www.cirget.uqam.ca/fr/seminaires.html

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The recorded talks can be found at CIRGET channel : www.youtube.com/channel/UCLkFm-uEvXSf9y-iQtWOLWA