- Series
- ACO Student Seminar
- Time
- Friday, February 22, 2013 - 1:05pm for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Matt Baker – School of Mathematics, Georgia Tech – http://people.math.gatech.edu/~mbaker/
- Organizer
- Chun-hung Liu
We will begin by formulating the Riemann-Roch theorem for graphs, due to
the speaker and Norine. We will then describe some refinements and
applications.
Refinements include a Riemann-Roch theorem for tropical curves, proved
by Gathmann-Kerber and Mikhalkin-Zharkov, and a Riemann-Roch theorem for
metrized complexes of curves, proved by Amini and the speaker.
Applications include a new proof by Cools-Draisma-Payne-Robeva of the
Brill-Noether theorem in algebraic geometry, a generalization by Amini
and the speaker of the Eisenbud-Harris theory of limit linear series,
and a new Chabauty-Coleman style bound for the number of rational points
on an algebraic curve over the rationals, proved recently by Katz and
Zureick-Brown.