### Tropical schemes, tropical cycles, and valuated matroids

- Series
- Algebra Seminar
- Time
- Monday, November 4, 2013 - 16:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Diane Maclagan – University of Warwick

The tropical cycle associated to a subvariety of a torus is the support of a weighted polyhedral complex that that records information
about the original variety and its compactifications. In a recent preprint Jeff and Noah Giansiracusa introduced a notion of scheme
structure for tropical varieties, and showed that the tropical variety as a set is determined by this tropical scheme structure. I will outline how
to also recover the tropical cycle from this information. This involves defining a variant of Grobner theory for congruences on the semiring of
tropical Laurent polynomials. The lurking combinatorics is that of valuated matroids. This is joint work with Felipe Rincon.