Alex Fink

Stiefel tropical linear spaces

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.