Consortium Distinguished Lecture Series
Andras Szenes
Intersection Cohomology of the Moduli Spaces of Stable Bundle I
Andras Szenes, University of Geneva
Thursday, March 9, 2023, 5:00pm
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Abstract: Intersection cohomology is a topological notion adapted to the description of singular topological spaces, and the Decomposition Theorem for maps is a key tool in the subject. The study of the intersection cohomology of the moduli spaces of semistable bundles on Riemann surfaces began in the 80’s with the works of Frances Kirwan. Motivated by the work of Mozgovoy and Reineke, in joint work with Camilla Felisetti and Olga Trapeznikova, we give a complete description of these structures via a detailed analysis of the Decomposition Theorem applied to a certain map. We also give a new formula for the intersection Betti numbers of these moduli spaces, which has a clear geometric meaning. In these talk, I will give an introduction to the subject, and describe our results.
Intersection Cohomology of the Moduli Spaces of Stable Bundle II
Andras Szenes, University of Geneva
Friday, March 10, 2023, 5:00pm
Click Here to view video
Abstract: Intersection cohomology is a topological notion adapted to the description of singular topological spaces, and the Decomposition Theorem for maps is a key tool in the subject. The study of the intersection cohomology of the moduli spaces of semistable bundles on Riemann surfaces began in the 80’s with the works of Frances Kirwan. Motivated by the work of Mozgovoy and Reineke, in joint work with Camilla Felisetti and Olga Trapeznikova, we give a complete description of these structures via a detailed analysis of the Decomposition Theorem applied to a certain map. We also give a new formula for the intersection Betti numbers of these moduli spaces, which has a clear geometric meaning. In these talk, I will give an introduction to the subject, and describe our results.
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