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Algebra and Geometry Seminar

Date:
-
Location:
POT 745
Speaker(s) / Presenter(s):
Jeff Giansiracusa
Semirings and schemes in tropical geometry
 
The tropicalization of a variety is usually considered as a polyhedral set inside Euclidean space, but people often think of it heuristically as an algebraic set defined over the idempotent semiring of real numbers with the (max,+) structure.  I'll explain how to give this heuristic picture teeth: it turns out that the tropicalization trop(X) is actually the solution set to a system of (max,+) polynomial equations canonically associated with X.   This leads to tropical Hilbert polynomials and several other interesting things.