Title: A Survey of Tropical Cohomology
Speaker: Kyle Binder (OSU)
Speaker's URL: https://math.osu.edu/people/binder.65
Abstract: Tropical homology and cohomology arose as a way to study the Hodge structure of a family of complex projective varieties in passing to a tropical limit. For tropical varieties coming from complex hyperplane arrangement complements, tropical cohomology allows one to compute the de Rham cohomology of the hyperplane arrangement complement in a combinatorial way. As a cohomology theory germane to tropical geometry, tropical cohomology is interesting to study in its own right, with analogues of Poincare duality and the Lefschetz (1,1)-Theorem.
In this expository talk, I will introduce tropical cohomology, the various ways of computing cohomology, and some interesting properties. Throughout the talk I will give examples and specific computations.
URL associated with Seminar: https://research.math.osu.edu/agseminar/