### GRT at home Seminar

Yaping Yang, University of Melbourne

Cohomological Hall algebras and perverse coherent sheaves on toric Calabi-Yau 3-folds

Organizer's time: 2020-06-23 10:00 Europe/Rome

Duration: 1 hour 30 minutes

Access information: zoom: 842 5923 2669

I will talk about cohomological Hall algebras (COHA) of toric Calabi-Yau 3-folds and their representations. Let $X$ be a smooth local toric Calabi-Yau 3-fold. On the cohomology of the moduli spaces of certain sheaves (e.g. torsion free sheaves, or sheaves supported on a toric divisor) on X, there is an action of the COHA of Kontsevich and Soibelman via “raising operators”. I will discuss the “double” of the COHA that acts on the cohomology of the moduli space by adding the “lowering operators”. We associate a root system to $X$. The double COHA is expected to be the shifted Yangian of this root system. We also give a prediction for the shift in terms of an intersection pairing. We provide evidence of the aforementioned expectation in various examples.