University of Washington, Spring 2020

Math 563 -- Graphs and Tropical Curves


Farbod Shokrieh

Lecture time and address:

MWF 12:30-13:20PM
Zoom Meeting ID: email me if you don't have it already.
Office hours: Wednesdays 3--5pm. Also by appointment, email me

Lecture notes:

I will upload my handwritten notes to a folder in Google Drive and share the link with you.


We will discuss some fundamental results on both finite and metric graphs (abstract tropical curves). We will also present a few open problems along the way, some of which might be within reach for strong undergraduate or graduate students.

Advanced topics might include: Metric Graphs and Tropical Curves, Chip-Firing Games, Abel-Jacobi and Riemann- Roch Theory on Graphs, Potential Theory, and maybe even some recent applications in Algebraic Geometry and Number Theory.

Course requirements:

Students will study and present topics that compliment the material presented in lectures, and will write a short expository article. Obviously, the final paper does not have to be expository, and you are welcome to solve some of the open problems that I propose instead.

I expect you to attend most classes and participate actively in class disccussions. If at some point you decide to stop coming to class, please drop the course.



There is no official textbook. We use various sources, including several research papers.

Some books:

Some papers:

Digital copies of these references can be found in the Google Drive folder.

Disability Resources and Accommodations:

Reasonable accommodations will be provided to students who have a documented disability that may affect their ability to participate in course activities or to meet course requirements. Students with disabilities are encouraged to contact the office of Disability Resources for Students (DRS).

Religious Accommodations::

Washington state law requires that UW develop a policy for accommodation of student absences or significant hardship due to reasons of faith or conscience, or for organized religious activities. The UW's policy, including more information about how to request an accommodation, is available at Religious Accommodations Policy. Accommodations must be requested within the first two weeks of this course using the Religious Accommodations Request form.

Academic Integrity:

Each student in this course is expected to abide by the University of Washington's code of academic integrity. Any work submitted by a student in this course for academic credit will be the student's own work. More information about this code is available here.

Intellectual Property and Copyright:

All course materials are intellectual property belonging to the author. Students are not permitted to share any course materials without the expressed permission of the instructor.

(Last modified on: June 15, 2020)