**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.