### Stiefel tropical linear spaces

Algebra and Geometry Seminar

31st May 2018, 1:00 pm – 2:00 pm

Howard House, 4th Floor Seminar Room

As we tell our undergraduates, over a field K there are a great number of ways

to describe a linear subspace of K^n. Over the tropical semiring, many of

these cease to agree, but tropical geometers have a consensus as to which of

them give the correct notion of tropical linear subspace (one that does is

Pl\"ucker vectors). My subject will be one of the "wrong" descriptions, namely

row spaces of matrices, which give a subset of the tropical linear spaces.

Applications will include a tropical-valued generalisation of Mason's results

from the '70s on presentations of transversal matroids and constructions in the

new field of tropical ideal theory.

Most of this work is joint with Felipe Rincón; other parts are joint with

Jorge Alberto Olarte or Jeffrey and Noah Giansiracusa.

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