Matroids and Tropical Geometry
Introductory Workshop: Geometric and Topological Combinatorics September 05, 2017 - September 08, 2017
Location: MSRI: Simons Auditorium
52B40 - Matroids (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.) [See also 05B35, 52Cxx]
14T05 - Tropical geometry [See also 12K10, 14M25, 14N10, 52B20]
Tropical algebraic geometry studies varieties by `tropicalizing' them into polyhedral complexes. The hope, which is realized surprisingly often, is that difficult algebro-geometric questions will reduce to simpler polyhedral questions. The resulting questions are usually not easy, and that’s good news for us: they have led to several new and interesting research directions in geometric combinatorics. Matroids often play a fundamental role because they are equivalent to tropical linear spaces. This talk will survey a few central aspects of the interplay between matroids and tropical geometry, and discuss some recent developments.
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