Math 648: Tropical geometry

This course will be an introduction to tropical geometry. Our textbook will be the in prepration draft of Introduction to Tropical Geometry by Diane Maclagan and Bernd Sturmfels, which is freely available here. Coursework will consist of bi-weekly homeworks together with final projects in the last third of the semester. For details, see the course syllabus.

Course times



Homework is due every other Tuesday and the assignments will be posted here.


The approximate schedule for future classes is as follows. All reading assignments are from Introduction to Tropical Geometry.

Jan. 211.1,1.3tropical curves
Jan. 232.3polyhedral geometry
Jan. 282.1,2.2valued fields, algebraic varieties
Jan. 302.4Gröbner bases
Feb. 42.4Gröbner bases, cont.
Feb. 62.5Gröbner complexes
Feb. 112.6tropical bases
Feb. 133.2fundamental theorem
Feb. 183.3Bieri-Groves
Feb. 203.4multiplicities
Feb. 253.4balancing
Feb. 273.5connectivity
Mar. 44.1hyperplane arrangements
Mar. 64.1fine subdivision
Mar. 254.2matroids
Mar. 274.2matroids
Apr. 84.3Grassmannians
Apr. 104.3,3.6Grassmannians, stable intersection
Apr. 154.6mixed volumes
Apr. 17lifting problems
Apr. 22smooth surfaces
Apr. 24presentations: Daping, Dylan, Vesslin
Apr. 29presentations: Tiff, Yoav, Dhruv
May 1presentations: Dan, Rodrigo, Shaked