Final Project

For the final project of this class, you will give a 20-30 minute presentation in class and write a paper. The topic can be an exposition of a topic related to tropical geometry, such as a research paper of book chapter. You should contribute something new to the exposition, such as a new example (or a new theorem!). There is no formal length requirement for the paper, but it should be long enough to give a coherent exposition of your topic. Only one student can work on a given paper and projects will be assigned as requested. The project timeline is the following:

Topic choice by February 10
Student presentations: In class, March 4, 6, 11, 13 and March 19 (finals slot, 10:30am-12:30pm)
Final paper due March 19

Schedule (tentative)
Tues. March 4: Mont, Dhruv
Thurs. March 6: Cameron, Lauren
Tues. March 11: Tracy, Joe, Garcia
Thurs. March 13: Patrick, Freda, Zihong
Wed. March 19: Natasha, Michael, Varun, Jenny

Projects (so far)

Dhruv Bhatia: Embedded to abstract tropical curves, after Chan and/or Baker-Len-Morrison-Pflueger-Ren
Tracy Chin: Real tropicalization and analytification of semialgebraic sets, after Jell-Scheiderer-Yu
Mont Cordero: Tropical Intersection Theory, after Ardila-Cordero and Ardila-Klivans
Natasha Crepeau: Jacobians of Tropical Curves, after Mikhalkin-Zharkov
Zihong Lin: Connections with toric geometry
Lauren Novak: Oriented matroids, after Ardila-Develin
Patrick O'Melveny: Combinatorial Hodge Theory, after Adiprasito-Huh-Katz and Amini-Pirquerez
Joe Rogge: The tropical totally positive Grassmannian, after Speyer-Williams
Varun Shah: Tropical Geometry of Statistical Models, after Pachter-Sturmfels and Zwang-Naitzat-Lim
Garcia Sun: Tropical Polyhedra and Mean Payoff Games, after Akian-Gaubert-Guterman
Cameron Wright: Matroids over Perfect Idylls, after Jarra-Lorscheid-Vital and Iezzi-Schleis
Michael Zeng: Tropical bitangents, after Markwig-Payne-Shaw
Jenny Zhan: Product-mix auctions and tropical geometry, after Tran-Yu
Freda Zhang: Applications of tropical geometry to the monodromy conjecture, after Bories-Veys