Jump To中央區塊/Main Content :::
:::

Seminars

Special Colloquium

From Enumerative Geometry to Representation Theory, and Back, via Cohomological Hall Algebras

2026/01/22 (Thu.) 15:30~16:30
  • Date : 2026/01/22 (Thu.) 15:30~16:30
  • Location : Seminar Room 638, Institute of Mathematics (NTU Campus)
  • Speaker : Francesco Sala (University of Pisa)
  • Abstract :
    In 2012, Schiffmann-Vasserot and Maulik-Okounkov independently proved that the equivariant cohomology of the rank-r ADHM moduli space carries the structure of a Verma module of the principal affine W-algebra W(gl(r)), proving a part of the Alday-Gaiotto-Tachikawa conjectures. These conjectures relate Nekrasov partition functions of four-dimensional gauge theories to conformal blocks of two-dimensional conformal field theories.
    These works have had a lasting impact, also because of the diversity of techniques used in their proofs. In both approaches, the vertex algebra action arises from an action of the affine Yangian of gl(1), obtained through two a priori completely different geometric constructions. In particular, the work of Schiffmann-Vasserot makes essential use of the cohomological Hall algebra (COHA) of zero-dimensional coherent sheaves on the complex plane. During the first half of the talk, I will provide a gentle introduction to these ideas and results.

    In the second half of the talk, I will explain how a formulation of the theory of COHAs associated with smooth surfaces within the framework of derived algebraic geometry, developed in recent years in joint work with Duliu-Emanuel Diaconescu and Mauro Porta, has revealed new and intriguing connections between moduli spaces and stacks in algebraic geometry and the theory of Yangians in representation theory. These include, for example, a geometric realization of a family of nonstandard halves of affine Yangians over Bridgeland’s space of stability conditions. This part of the talk is based on joint work with Duliu-Emanuel Diaconescu, Mauro Porta, Olivier Schiffmann, and Eric Vasserot (arXiv:2502.19445), as well as joint work with Olivier Schiffmann and Parth Shimpi (arXiv:2511.08576).
:::
Resolving dependencies...