Math 665: Tropical Brill–Noether Theory

These are lecture notes for a seminar course led by David Jensen and Sam Payne at Yale University in Spring 2016. Seminar participants included Daniel Corey, Netanel Friedenberg, Oleksii Kislinskyi, Nikolay Malkin, Dhruv Ranganathan, Jifeng (Tif) Shen, Jeremy Usatine, and Nicholas Wawrykow.

Notes for each lecture were taken by Friedenberg, and revised by Jensen, Payne, and the speaker, with input from all participants.

- Lecture 1: Divisors on Graphs (David Jensen)
- Lecture 2: Reduced Divisors (Sam Payne)
- Lecture 3: Riemann–Roch (Nikolay Malkin)
- Lecture 4: Rank-Determining Sets (Nicholas Wawrykow)
- Lecture 5: Special Divisors on a Chain of Loops (Daniel Corey)
- Lecture 6: Riemann-Hurwitz Theory for Graphs (Dhruv Ranganathan)
- Lecture 7: Specialization of Divisors from Curves to Graphs (Jeremy Usatine)
- Lecture 8: Divisor Theory of Metric Graphs (David Jensen)
- Lecture 9: Jacobians of Metric Graphs (Tif Shen)
- Lecture 10: Clifford's Theorem (Nicholas Wawrykow)
- Lecture 11: Analytifications and skeletons of curves (Jeremy Usatine)
- Lecture 12: Tropical proof of the Brill–Noether theorem (Oleksii Kislinskyi)
- Lecture 13: Tropical proof of the Gieseker–Petri theorem (Nikolay Malkin)
- Lecture 14: Uniformization of curves (Asher Auel)
- Lecture 15: The Tropicalization of the Jacobian is the Jacobian of the Tropicalization (Tif Shen)
- Lecture 16: Lifting tropical intersections (Dhruv Ranganathan)
- Lecture 17: Lifting special divisors on a chain of loops (Daniel Corey)