Abstract for the talk on 21.11.2017 (11:00 h)Seminar on Nonlinear Algebra
Emanuele Delucchi (Université de Fribourg)
Not really linear algebra
Matroids over hyperfields, introduced by Baker and Bowler in 2016, offer a new unifying vision encompassing matroids, vector spaces, and related ideas in tropical geometry. The key tool are hyperfields, i.e., algebraic structures akin to fields — but with multivalued addition.
In this talk I will define matroids over hyperfields, present some examples (especially as related to tropical geometry and oriented matroids) and I will discuss some of the first results in this very young subject (which can be understood as looking for a “linear algebra” over hyperfields). The exposition will not presuppose any special previous knowledge.