**Ashwin Deopurkar**

TIFR, Mumbai

November 2, 2017

**Tropical geometry of curves**:
Perhaps surprisingly, the study of degenerate curves plays a crucial role in our understanding of a general smooth curve. One of the first successes of this idea was the theory of limit linear series developed by Griffiths and Harris which they used to prove the Brill-Noether theorem. The analogous theory for degenerate curves of non-compact type falls in the realm of tropical geometry where it takes the shape of metric graphs (or tropical curves) and divisors on them. This leads to a rich interplay between graph theory and algebraic geometry of curves. After explaining the central ideas we will discuss some applications to Brill-Noether theory and curves of large theta characteristic.