Algebraic Geometry Seminar

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A Glimpse of Supertropical Algebra and Its Applications

Speaker: Zur Izhakian, University of Aberdeen and University of Bremen

Location: Warren Weaver Hall 1314

Date: Thursday, May 8, 2014, 11 a.m.

Synopsis:

Tropical mathematics is carried out over idempotent semirings, a weak algebraic structure that on the one hand, allows descriptions of objects having a discrete nature, but on the other, its lack of additive inverse prevents access to some basic mathematical notions. These drawbacks are overcome by use of a supertropical semiring -- a ``cover'' semiring structure having a special distinguished ideal that plays the role of the zero element in classical mathematics. This semiring structure is rich enough to enable a systematic development of tropical algebraic theory, yielding direct analogues to many important results and notions from classical commutative algebra. Supertropical algebra provides a suitable algebraic framework that enables natural realizations of matroids and simplicial complexes, as well as representations of semigroups.