Derived Approach to Highest Weight Categories

Explore the intricacies of highest weight categories in this 1-hour 10-minute lecture by Alexey Bondal at BIMSA. Delve into the abstract interpretation of categories of perverse sheaves on stratified topological spaces with contracted strata, and discover their significance in Representation Theory. Examine how highest weight categories and Ringel duality can be understood through exact categories, abelian envelops, and exceptional collections in derived categories. Investigate the fascinating applications of highest weight categories in Birational Geometry, particularly their role as abelian null-categories of birational morphisms. Learn about the technique's ability to identify the derived support of the null-category for smooth surface contractions as the discrepancy divisor, and consider the potential extension of this concept to higher dimensions.