Colloquium abstracts

Madhusudan Manjunath
IIT, Mumbai
March 8, 2018

Riemann-Roch, Graphs, Lattices and Free Resolutions:  The Riemann-Roch theorem is fundamental to algebraic geometry. In 2006, Baker and Norine discovered an analogue of the Riemann-Roch theorem for graphs. In fact, this theorem is not a mere analogue but has concrete relations with its algebro-geometric counterpart. Since its conception this topic has been explored in different directions, two significant directions are i. Connections to topics in discrete geometry and commutative algebra ii. As a tool to studying linear series on algebraic curves. We will provide a glimpse of these developments. This talk is based on joint work with i. Omid Amini, ii. Bernd Sturmfels, iii. Frank-Olaf Schreyer and John Wilmes.