Welcome to our new seminar series in Combinatorial Algebraic Geometry taking place on Mondays 14:00-15:30 on Zoom. 

Goal: 

Hodge theory is a classical and powerful tool in algebraic and arithmetic geometry, which has been widely used in various theories including, but not limited to, cohomologies, moduli spaces (Torelli theorems), mirror symmetry, and finiteness of rational points (Faltings theorem). Our focus in this seminar series is to read some recent works of June Huh and collabrators on the Hodge structure on matroids, or combinatorics Hodge theory. In particular, we will go through the proofs of Rota-Welsh log-concavity conjecture in detail.

References:

[1] Adiprasito-Huh-Katz: Hodge Theory for Combinatorial Geometries (link)

[2] Baker: Hodge Theory in Combinatorics (link)

[3] Wang: Hodge Theory for Matroids (link)

[4] Adiprasito-Huh-Katz: Hodge Theory of Matroids (link)

[5] Katz: Matroid Theory for Algebraic Geometers (link)

[6] Antoine Chambert-Loir: Relations de Hodge--Riemann et Combinatoire des Matroïdes (d'après K. Adiprasito, J. Huh et E. Katz) (link)

Registration

Please email Fatemeh if you are interested in attending the meeting. I will email you the link/password on the day of the meeting.

Tentative Schedule:

• February 21, 2022:  Xian Wu (Notes)

• February 28, 2022:  Xian Wu (Notes)

• March 7, 2022: Francesca Zaffalon (Notes)

• March 14, 2022: Ayush Kumar Tewari (Notes)

• March 21, 2022: Ayush Kumar Tewari

• March 28, 2022: Ayush Kumar Tewari

• April 4, 2022: Ahmed Umer Ashraf (Notes)

• April 11, 2022: Xian Wu (Notes)

• April 25, 2022: Oliver Clarke (Notes)

Organizer: Fatemeh Mohammadi