Minicourse: Linearity in the tropics I
Saturday August 22, 2009
09:30AM - 10:30AM
Speakers:
Federico Ardila
Abstract:
Tropical geometry studies an algebraic variety X by `tropicalizing' it into a polyhedral complex Trop(X) which retains some information about X. Tropical varieties may be simpler than algebraic varieties, but they are by no means well understood. In fact, tropical linear spaces already feature a surprisingly rich and beautiful combinatorial structure, and interesting connections to geometry, topology, and phylogenetics. I will discuss what we currently know about them.
In the first lecture, I will give a introduction to matroids, and explain how they describe the local structure of a tropical linear space, both combinatorially and topologically. In the second lecture I will explain the correspondence between tropical linear spaces and the subdivisions of a matroid polytope into smaller matroid polytopes, and discuss the tropical Grassmannian.
Some exercises will be given out between the two talks.
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