### DIMACS Special Seminar

Title: Tropical Geometry

Speaker: **Tristram Bogart**, University of Washington

Date: Friday, March 9, 2007 10:15 am

Location: DIMACS Center, CoRE Bldg, Room 431, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

Tropical geometry is the geometry associated to the
algebra of real numbers with the operations of minimum and addition.
Using this algebra, a "tropical variety" can be associated to any ideal
in a polynomial ring over an algebraically closed field. Tropical
varieties are polyhedral complexes, hence can be studied
combinatorially, while also satisfying familiar rules of algebraic
geometry such as Bezout's Theorem.

I will introduce tropical geometry, discuss applications to dynamics
and the theory of algebraic curves, present key results from a joint
paper with Anders Jensen, David Speyer, Bernd Sturmfels, and Rekha
Thomas, and finally discuss my current studies in the area.