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.