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
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I will talk about cohomological Hall algebras (COHA) of toric Calabi-Yau 3-folds and their representations. Let 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 . 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.
This is based on my joint work with M. Rapcak, Y. Soibelman, and G. Zhao.
Video is here
Slides are here
Submitted by: Francesco Sala