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.
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. 21||1.1,1.3||tropical curves|
|Jan. 23||2.3||polyhedral geometry|
|Jan. 28||2.1,2.2||valued fields, algebraic varieties|
|Jan. 30||2.4||Gröbner bases|
|Feb. 4||2.4||Gröbner bases, cont.|
|Feb. 6||2.5||Gröbner complexes|
|Feb. 11||2.6||tropical bases|
|Feb. 13||3.2||fundamental theorem|
|Mar. 4||4.1||hyperplane arrangements|
|Mar. 6||4.1||fine subdivision|
|Apr. 10||4.3,3.6||Grassmannians, stable intersection|
|Apr. 15||4.6||mixed volumes|
|Apr. 17||lifting problems|
|Apr. 22||smooth surfaces|
|Apr. 24||presentations: Daping, Dylan, Vesslin|
|Apr. 29||presentations: Tiff, Yoav, Dhruv|
|May 1||presentations: Dan, Rodrigo, Shaked|