Ilia Zharkov

Tropical curves and their Jacobians

Abstract: I will give an introduction into the subject of tropical geometry. Then I will describe tropical analogues of geometric objects classically associated with algebraic curves: divisors, line bundles, Jacobians, Theta functions and state the tropical counterparts of some clasical theorems such as Abel-Jacobi, Riemann-Roch and Riemann theta divisor. Based on a joint work with Grisha Mikhalkin.