Chennai Mathematical Institute


3:30 pm, Lecture Hall 1
A tropical proof of the Brill-Noether theorem

Dhruv Ranganthan
University of Cambridge.


The Brill-Noether theorem gives complete control of the linear systems on a general algebraic curve and was proved by Griffiths and Harris in the 1980s. I will present a proof of this theorem that is based on tropical methods, explaining in detail the translation from algebraic geometry to combinatorics, and outlining the solution to the resulting combinatorial problem. This proof is due to Cools, Draisma, Payne, and Robeva in 2012, based on a 2008 conjecture of Baker. Time permitting, I will give a sense for generalizations and more recent developments.

This is technically the second in a series of talks, but I will not assume anything substantial from the first lecture.