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
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.