Intersection Cohomology of the Moduli Spaces of Stable Bundle I

Explore the intricacies of intersection cohomology and its application to moduli spaces of semistable bundles on Riemann surfaces in this comprehensive lecture. Delve into the groundbreaking work of Frances Kirwan from the 1980s and discover recent advancements made by Mozgovoy and Reineke. Learn about the collaborative research conducted by Andras Szenes, Camilla Felisetti, and Olga Trapeznikova, which provides a complete description of these structures through a detailed analysis of the Decomposition Theorem. Gain insights into a new formula for calculating intersection Betti numbers of moduli spaces, understanding its geometric significance. This one-hour lecture, part of the Consortium Distinguished Lecture Series, serves as an introduction to the subject and presents the latest findings in the field of algebraic topology and geometry.