25.06.2019 um 16:15 Uhr in 69/125:
Jose Alejandro Samper (MPI Leipzig)
Slicing matroid polytopes
We introduce the notion of a matroid threshold hypergraph: a set system obtained by slicing a matroid basis polytope and keeping the bases on one side. These hypergraphs can be then used to define a class of objects that slightly extends matroids and has a few new techincal advantages. For example, it is amenable to several inductive procedures that are out of reach to matroid theory. In this talk we will motivate the study of these families of hypergraphs, relate it to some old open questions and pose some new conjectures. To conclude we will show that the study of these objects helps us find a link between the geometry of the normal fan of the matroid polytope and shellability invariants/activities of independence complexes.
19.06.2019 um 14:15 Uhr in 69/E15:
Alberto Navarro Garmendia (University of Zürich)
Recent developments in the Riemann-Roch theorem
In this talk we will review some classic questions posed by Grothendieck and others around the Riemann-Roch theorem. Afterwards, we will explain how the Riemann-Roch fits into Panin's orientation theory and how motivic homotopy theory and Gabber's work on absolute purity have developed the Riemann-Roch theorem. Finally, we will speak about the lift of the Riemann-Roch into integral coefficients.