Cohomological Hall Algebras and Perverse Coherent Sheaves on Toric Calabi-Yau 3-Folds

Explore a 41-minute lecture from the Workshop on Representation Theory, Calabi-Yau Manifolds, and Mirror Symmetry where mathematical concepts involving cohomological Hall algebras (COHA) and their relationship with smooth local toric Calabi-Yau 3-folds are examined. Delve into the action of COHA on the cohomology of moduli spaces of sheaves through raising operators, and discover the double COHA's role in introducing lowering operators. Learn about the root system associated with toric Calabi-Yau 3-folds and understand how the double COHA is predicted to function as the shifted Yangian of this system. Examine the shift prediction in terms of intersection pairing and explore various examples supporting these mathematical relationships.