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- D. Speyer, Bernd Sturmfels
- 2003

In tropical algebraic geometry, the solution sets of polynomial equations are piecewise-linear. We introduce the tropical variety of a polynomial ideal, and we identify it with a polyhedral subcomplex of the Gröbner fan. The tropical Grassmannian arises in this manner from the ideal of quadratic Plücker relations. It is shown to parametrize all tropical… (More)

- Tristram Bogart, Anders Nedergaard Jensen, D. Speyer, Bernd Sturmfels, Rekha R. Thomas
- J. Symb. Comput.
- 2007

In this paper we use toric geometry to investigate the topology of the totally non-negative part of the Grassmannian, denoted (Grk,n)≥0. This is a cell complex whose cells G can be parameterized in terms of the combinatorics of plane-bipartite graphs G. To each cell G we associate a certain polytope P(G). The polytopes P(G) are analogous to the well-known… (More)

- Kelli Talaska, Samuel Epstein, +23 authors Terry McCabe
- 2010

This dissertation is dedicated to the memory of my mother, Kathleen Marie Harter. ii ACKNOWLEDGEMENTS I have come this far largely because I have had a great deal of support, encouragement , and companionship from amazing teachers, friends, and colleagues, and I would like to take this opportunity to thank some of those people. Graduate school at Michigan… (More)

Tropical Geometry by David E Speyer Doctor of Philosophy in Mathematics University of California, Berkeley Professor Bernd Sturmfels, Chair Let K be an algebraically closed field complete with respect to a nonarchimedean valuation v : K∗ → R. The reader should think ofK as the field of Puiseux series, ⋃∞ n=1 C((t )) and v as the map that assigns to a power… (More)

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