Andreas Hochenegger - Politecnico di Milano

Cohomology of toric vector bundles via Weil decorations

One can write divisors D as a difference of two nef divisors. In the toric context, this translates into the formal difference of two polytopes P-Q. It is possible to express the cohomology of O(D) via these two polytopes. In my talk I will show how this approach can be generalized to vector bundles E of higher rank. Using the language of Weil decorations, the cohomology of E will be related to the cohomology of a constructible sheaf. This is joint work with Klaus Altmann and Frederik Witt.

Mima Stanojkovski - Università di Trento
Stable lattices in Bruhat-Tits buildings: algebra, geometry, and combinatorics

Let K be a discretely valued field with ring of integers R and let d be a positive integer. Then the rank d free R-submodules of K^d (called R-lattices) are the 0-simplices of an infinite simplicial complex called a Bruhat-Tits building. If O is an order in the ring of dxd matrices over K, then the collection of lattices that are also O-modules (called O-lattices) is a non-empty, bounded and convex subset of the building. Determining what these subsets are is in general a difficult question.
I will report on joint work with Yassine El Maazouz, Gabriele Nebe, Marvin Hahn, and Bernd Sturmfels describing the geometric and combinatorial features of the set of O-lattices for some particular orders.