Hodge theory in combinatorial geometry

Speaker:Botong Wang (University of Wisconsin-Madison)
Schedule:Mon. & Wed. & Fri., 1:30 - 3:30pm.
Venue:No.4 Teaching Building, Room 102 (9-4/6/8), Room 103 (9-11/13)
Title: Hodge theory in combinatorial geometry.

Abstract: The purpose of these lectures is to give a survey on the recent resolution of two conjectures in matroid theory. The first one is the Heron-Rota-Welsh conjecture by Adiprasito-Huh-Katz, and the second one is the Dowling-Wilson conjecture by Braden-Huh-Matherne-Proudfoot-Wang. The main idea is to attach algebraic geometric invariants to a given matroid, and use ideas from Hodge theory to derive combinatorial properties. If time permits, we will also survey some ongoing developments of intersection cohomology of matroids and some new applications.

Course video playback:

Date: 2023-09-04
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Date: 2023-09-06

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Date: 2023-09-08

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Date: 2023-09-11
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Date: 2023-09-13
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