Hodge theory for tropical varieties 1

Algebra Seminar
Wednesday, November 11, 2020 - 3:30pm for 1 hour (actually 50 minutes)
Matthieu Piquerez
Justin Chen

Please Note: Part 1 of 3-part series

The aim of these two talks is to give an overview of our work on tropical Hodge theory. We show that cohomology groups of smooth projective tropical varieties verify hard Lefschetz property and Hodge-Riemann relations. Providing a description of the Chow groups of matroids in terms of cohomology groups of specific smooth projective tropical varieties, these results can be regarded as a generalization of the work of Adiprasito-Huh-Katz to more general tropical varieties. We also prove that smooth projective tropical varieties verify the analogue in the tropical setting of the weight-monodromy conjecture, affirming a conjecture of Mikhalkin and Zharkov.

BlueJeans link: https://bluejeans.com/476849994