Seminar
A guided introduction to intersection homology and applications: Lecture 1.
, Dr. Laurentiu Maxim , University of Wisconsin, Madison, Fri, 2 May, 2025, 4:00 p.m. CN-142
Abstract
Intersection homology was introduced by Goresky and MacPherson in order to recover some of the classical results and properties of manifolds (like Poincare duality, Lefschetz type theorems and Hodge theory for complex manifolds) in the context of singular spaces. The guiding principle of intersection homology is that these results hold once one considers only chains that meet the singular locus with a controlled lack of transversality.
- Lecture 1: (May 2, 2025, 4:00 – 5:00 pm, UPR-RP, CN-142) I will give a motivated introduction to intersection homology, by first recalling basic homological properties for manifolds, and then illustrating by examples how these properties can be restored in the singular context.
- Lecture 2: (May 3, 2025, 10:30-11:30 am, UPR-RP, CN-142) I will give a second definition of intersection homology using sheaves, and discuss the Kaehler package for the intersection homology groups of complex projective varieties.
- Lecture 3: (May 3, 2025, 2:30 – 3:30 pm, UPR-RP, CN-142) I will briefly indicate several applications of intersection homology: (i) for studying the topology of Hilbert schemes of points on smooth complex surfaces; (ii) Stanley’s proof of McMullen’s conjecture, describing the existence of a simplicial polytope with a prescribed face vector; and (iii) Huh-Wang’s proof of Dowling-Wilson’s conjecture for realizable matroids.
This event is part of the Algebraic structures in topology conference series sponsored by the National Science Foundation.
Post is here.
