Algebraic Geometry Seminar
Cohomological Hall algebras of 1-dimensional sheaves and Yangians
2026/01/21 (Wed.) 14:00~16:00
- Date : 2026/01/21 (Wed.) 14:00~16:00
- Location : Seminar Room 617, Institute of Mathematics (NTU Campus)
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Speaker : Francesco Sala (University of Pisa)
- Abstract :
The first part of this talk provides a brief and gentle introduction to the theory of two-dimensional cohomological Hall algebras of quivers and surfaces, focusing on the construction of these algebraic structures and the main results concerning them.
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 that are set-theoretically supported on a closed subscheme Z. This algebra can be viewed as the "largest" algebra of cohomological Hecke operators associated with modifications along a subscheme Z of S. 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) in terms of the Yangian of the corresponding affine ADE quiver (based on arXiv:2502.19445, joint work with Emanuel Diaconescu, Mauro Porta, Oliver Schiffmann, and Eric Vasserot).
