Felipe Rincón (Berkeley) [Department of Mathematics and Statistics, Binghamton University]

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====== Felipe Rincón (Berkeley) ======

====== Computing Tropical Linear Spaces and A-Discriminants ======

===== Abstract for the Combinatorics Seminar 2011 May 3 =====

Tropical geometry studies an algebraic variety //X// by 'tropicalizing' it into a polyhedral complex that retains much of the information about //X//. In the case where //X// is a linear space the resulting polyhedral complex has a beautiful combinatorial structure related to the matroid of //X//, and for many applications it is desirable to have an explicit description of what this complex is.

In this talk I will give a quick introduction to tropical geometry and tropical linear spaces, and I will explain how they can be used to get a handle on classical //A//-discriminants. Also, I will describe an effective algorithm for computing the tropicalization of a linear space. There will be several examples, pictures, and software demonstrations.

No previous knowledge of tropical geometry (or discriminants) will be assumed.


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