## November 2017

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.

Abstract: I will discuss the application of the method of compensated compactness to the compressible, isentropic Euler equations under certain geometric assumptions, e.g. the case of fluid flow in a nozzle of varying cross-sectional area or the assumption of planar symmetry under special relativity. Under these assumptions, the equations reduce to the classical (or relativistic) one-dimensional isentropic Euler equations with additional geometric source terms. In this talk, I will explain how the classical strategy of DiPerna, Chen et. al. can be adapted to handle these more complicated systems and will highlight some of the difficulties involved in extending the techniques to the relativistic setting.

Vortrag in der Reihe: Arbeitsgemeinschaft ANGEWANDTE ANALYSIS

More information you can find on the conference homepage:

https://www.mis.mpg.de/calendar/conferences/2017/Berlin-LE-WS/index.html

Semi-algebraic sets of integer points.

We look at sets of integer points in the plane,

and discuss possible definitions of when such a set

is “complicated” — this might be the case if it

is not the set of integer solutions

to some system of polynomial equations and inequalities.

Let’s together work out lots of examples,

and on the way let’s try to develop criteria

and proof techniques …

The examples that motivated our study come

from polytope theory: Many question of the type

“What is the possible pairs of

(number of vertices, number of edges)

for 5-dimensional polytopes?”

have been asked, many of them with simple and complete

answers, but in other cases the answer looks complicated.

Our main result says: In some cases it IS complicated!

(Joint work with Hannah Sjöberg.)

More information you can find on the conference homepage:

https://www.mis.mpg.de/calendar/conferences/2017/Berlin-LE-WS/index.html