Cohomological Hall algebras of 1-dimensional sheaves and Yangians

Abstract: The first part of this talk provides a brief and gentle introduction to the theory of 2-dimensional cohomological Hall algebras. The second part focuses on the introduction of the nilpotent cohomological Hall algebra COHA(S, Z) of coherent sheaves on a smooth quasi-projective complex surface S set-theoretically supported on a closed subscheme Z. When S is the minimal resolution of an ADE singularity and Z is the exceptional divisor, I will describe how to characterize COHA(S, Z) via the Yangian of the corresponding affine ADE quiver. This is a joint project with Emanuel Diaconescu, Mauro Porta, Oliver Schiffmann, and Eric Vasserot.

algebraic geometryrepresentation theory

Audience: researchers in the topic

Algebra and Geometry Seminar @ HKUST

Series comments: Algebra and Geometry seminar at the Hong Kong University of Science and Technology (HKUST).

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