5 February 2025 — Padova

Yangians and cohomological Hall algebras

Francesco Sala, University of Pisa

Abstract

After a brief introduction to the theory of (2-dimensional) cohomological Hall algebras of quivers, curves, and surfaces, I will discuss the cohomological Hall algebra \(\mathsf{COHA}(S, Z)\) 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 \(\mathsf{COHA}(S, Z)\) via the Yangian of the corresponding affine ADE quiver. (joint project with Emanuel Diaconescu, Mauro Porta, Oliver Schiffmann, and Eric Vasserot.)