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Title: Tropical geometry of curves

Abstract: 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.

Ashwin Deopurkar, TIFR Mumbai