An invitation to research

I’m going to be speaking about “Spherical Varieties and Tropical Geometry” in the Invitation to Mathematics seminar in two successive weeks:

  • Wednesday, October 29, 2014 – 4:10pm to 5:10pm in Cockins Hall 218
  • Wednesday, November 5, 2014 – 4:10pm to 5:10pm in Cockins Hall 218

Here are lecture slides for my first talk. and my second talk.

Here’s my abstract:

This is intended as a prospectus of research, and I’m looking for students who want to work on this project. A complex algebraic variety is called a spherical variety if it’s acted upon by a reductive group and there is a dense orbit under the action of a Borel subgroup. To begin, I will explain some generalities about spherical varieties and the convex bodies associated to them, mostly via examples. Then I will focus on the research of Jason Miller, some of which appears in his 2014 Ohio State dissertation. Then, making a fresh start, I will say something about tropical varieties, which are piecewise linear or skeletal versions of algebraic varieties; again there will be examples. Tropical varieties naturally live in the world of toric varieties, which are extremely special examples of spherical varieties. The goal of the project is to find notions akin to those of tropical geometry in the wider world of spherical varieties.

For a related reading list, see my earlier post.

Reading list for tropical geometry and spherical varieties

(image by Cowdery and Challas, featured in June 2009 Mathematics Magazine)

This is a reading and viewing list for a small group of people who are working to learn these topics. Anyone is welcome to use it, of course.