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

• Lectures: TTh 2:30-3:45
• Classroom: LOM 200
• Office hours: see below for scheduled office hours
• Office: 219B LOM

Announcements

• May 1: Office hours 10-11am.
• Apr. 30: Office hours 2-4pm.
• Apr. 29: Office hours 10-11am, 1-2pm
• Apr. 28: No office hours
• Apr. 15: Make-up office hours 10-12am, 1-2pm.
• Apr. 14: No office hours.
• Mar. 31-Apr. 3: No office hours or class.
• Mar. 24: No office hours.
• Feb. 18: Office hours canceled.
• Jan. 13: Class will not meet during the first week of the semester. The first meeting will be on January 21.

Homeworks

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

• Problem set 1, due Feb. 11, 2014, last updated Feb. 9, 2014.
• Problem set 2, due Feb. 25, 2014.
• Problem set 3, due Mar. 25, 2014 (extended of original due date of Mar. 6).
• Problem set 4, due April 8, 2014.

Schedule

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

Date	Reading	Topics
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
Feb. 18	3.3	Bieri-Groves
Feb. 20	3.4	multiplicities
Feb. 25	3.4	balancing
Feb. 27	3.5	connectivity
Mar. 4	4.1	hyperplane arrangements
Mar. 6	4.1	fine subdivision
Mar. 25	4.2	matroids
Mar. 27	4.2	matroids
Apr. 8	4.3	Grassmannians
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