Here is a 3-paragraph summary of the blog post for mathopen.com:
This post introduces a set of draft lecture notes on the topic of Intersection Homology and Combinatorics, prepared for a talk at the Institute for Advanced Study (IAS). The lecture was scheduled for October 7 at 3:30 PM in the Seminar Room, giving the mathematical community a chance to explore the deep connections between two rich areas of mathematics. The notes were written under the author's guidance, with additional commentary highlighted in blue to provide extra context and insight.
Intersection homology is a powerful tool originally developed to extend Poincaré duality to spaces that are not smooth manifolds, such as singular algebraic varieties. When combined with combinatorics, these ideas open up surprising and elegant connections, linking abstract topological machinery to concrete counting problems and the structure of discrete objects like polytopes and partially ordered sets.
While the post itself is brief, serving mainly as an announcement and introduction to the lecture notes, it points to a fascinating area of modern mathematics where topology and combinatorics inform and enrich each other. Readers interested in algebraic topology, geometric combinatorics, or the geometry of singular spaces will find this an exciting topic worth exploring further.