Patchworking oriented matroids

Algebra Seminar
Wednesday, October 28, 2020 - 3:30pm for 1 hour (actually 50 minutes)
Location (To receive the password, please email Lutz Warnke)
Marcel Celaya – TU Berlin
Lutz Warnke

A classical result on oriented matroids due to Folkman and Lawrence in
1978 states that they are in bijection with pseudosphere arrangements up
to cellular homeomorphism. A more recent result, conjectured by Ardila and
Develin in 2007 and proved by Silke Horn in 2016, states that a similar
result holds for tropical oriented matroids and tropical hyperplane
arrangements. In a joint work with Georg Loho and Chi Ho Yuen, we show how
to unify these two results based on a variant of Viro's patchworking
technique, generalized to complete intersections by Sturmfels, for a
certain class of uniform oriented matroids arising from a product of two