[KAIST Discrete Math Seminar] 12/22 *WED* 4:30PM (HwanChul Yoo 유환철, Triangulations of Product of Simplices and Tropical Oriented Matroid)

[Sang-il Oum]

***** KAIST Discrete Math Seminar *****

DATE: December 22, Wednesday

TIME: 4:30PM-5:30PM

PLACE: E6-1, ROOM 3433

SPEAKER: HwanChul Yoo (유환철), Department of Mathematics, MIT

TITLE: Triangulations of Product of Simplices and Tropical Oriented Matroid

http://mathsci.kaist.ac.kr/~sangil/seminar/entry/20101222/

In 2006 at MSRI, nine tropical geometers and combinatorialists met and
announced the list of ten key open problems in (algebraic and
combinatorial side of) tropical geometry. Axiomatization of tropical
oriented matroids was one of them. After the work of Develin and
Sturmfels, tropical oriented matroids were conjectured to be in
bijection with subdivisions of product of simplices as well as with
tropical pseudohyperplane arrangements. Ardila and Develin defined
tropical oriented matroid, and showed one direction that tropical
oriented matroids encode subdivision of product of simplices.
Recently, in joint work with Oh, we proved that every triangulation of
product of simplices encodes a tropical oriented matroid.

In this talk, I will give a survey on this topic, and discuss this
well known conjecture. I will also suggest a new class of
combinatorial objects that may describe all subdivisions of a bigger
class of polytopes.

-- 
Sang-il Oum
Dept. of Mathematical Sciences, KAIST.
http://mathsci.kaist.ac.kr/~sangil/