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.

Link: https://unipd.zoom.us/j/82518660070?pwd=RUpxL1FnZG9yVzFrOCtrM0xYMEZaZz09

Meeting ID: 825 1866 0070

Password: 62542