Math 648 Projects

For the final portion of your grade, you should complete an independent project in tropical geometry. You may collaborate with one other person in the class, or work alone if you wish. Your project will consist of a written, typed, report as well as an in-class, 20 minute presentation. Deadlines:

• Wed, April 9: Have emailed me a 1 paragraph description of your proposed research project.
• Tue, April 24: First presentations
• Fri, May 2: Project report due

Your topic is up to you, but you must have your topic approved in advance. You may choose to investigate a research question or to read and present a paper in tropical geometry. Possible topics of either kind are the following, but feel free to choose your own topic:

• What is the possible topology of the transverse intersetion of two hypersurfaces in R³
• Are the faces of the matroid polytope of a graphic matroid also polytopes of graphic matroids?
• "Tropicalization of del Pezzo surfaces"
• Tropical schemes: "Equations of tropical varieties" and/or "Tropical schemes, tropical cycles, and valuated matroids"
• Tropical compactifications, chapter 12 of "A guide to tropicalizations"