This virtual seminar on topics that bridge combinatorics and geometry will be held on Zoom (usually) at 11:30-12:30 Eastern (Toronto) Time on the first Wednesday of every month. Complete this form to join our mailing list.
Upcoming seminars are listed below. Previous seminars are available on other tabs by year: 2024 or 2025 or 2026. Some recordings are available on the YouTube channel.
Ahmed Ashraf (University of Toronto, Mississauga)
Christin Bibby (Louisiana State University, Baton Rouge)
Graham Denham (Western University, London ON)
The Chow ring of a matroid was introduced by Adiprasito, Huh, and Katz as the Chow ring of the toric variety associated to the Bergman fan. This ring possesses several interesting properties such as satisfying Hard Lefschetz and (conjecturally) having a real-rooted Hilbert—Poincaré series.
In this talk, we introduce the singular cohomology ring of a matroid, which generalizes the Chow ring. It is defined as the singular cohomology ring of the toric variety associated to the Bergman fan. After giving an overview of the singular cohomology of smooth toric varieties, we draw out some of the analogies between the singular cohomology ring and the Chow ring of a matroid. In particular, we show for uniform matroids that these singular cohomology rings exhibit Lefschetz and real-rootedness properties similar to those of the Chow ring. This is based partially on joint work with Lorenzo Vecchi.