Workshop

This workshop will be part of MSRI's Special Semester in Hyperplane Arrangements and Applications. The combinatorial data associated with an arrangement of hyperplanes has proven to be core data for many algebraic and topological issues in arrangement theory. Conversely, the occurrence of certain combinatorial structures in arrangement theory has inspired research on generalizations in purely combinatorial settings. The following topics will be central to the presentations and discussions during this workshop: combinatorial models for arrangements oriented matroids combinatorics of arrangement compactifications phylogenetic trees topology of partially ordered sets combinatorial representation theory random walks on arrangements Confirmed speakers: Christos Athanasiadis Helene Barcelo Ken Brown Graham Denham Persi Diaconis Eva-Maria Feichtner Phil Hanlon Dmitry Kozlov Nikolai Mnev Alexander Postnikov Jessica Sidman Richard Stanley Hiroaki Terao Sasha Varchenko Anatoly Vershik Volkmar Welker Monday, November 1 8:30 - 9:15 Registration 9:15 - 9:30 Welcome and Introduction 9:30 - 10:30 Ken Brown Hyperplane face semigroups and their algebras. 10:30 - 11:00 Morning Tea (Sixth floor) 11:00 - 12:00 Persi Diaconis Are there q-deformations of hyperplanes that are useful for shuffling? 12:00 - 2:00 Lunch Break 3:00 - 4:00 Jessica Sidman, MSRI/Evans Lecture: Equations defining subspace arrangements. 4:15 – 5:00 Richard Stanley, MSRI/Evans Lecture The characteristic polynomial of a hyperplane arrangement. Tuesday, November 2 8:10 - 9:10 Bernd Sturmfels: Introduction to Matroid Polytopes 9:30 - 10:30 Eva-Maria Feichtner Nested set complexes in geometric combinatorics. 10:30 -11:00 Morning Tea (Sixth floor) 11:00 - 12:00 Dmitry Kozlov Combinatorics of DeConcini-Procesi resolutions of the real permutation action. 12:00 - 2:00 Lunch Break 2:00 - 3:00 Nicolai Mnev Combinatorial stratifications of the Grassmanians: algebraic geometry and combinatorial fiber bundles. 3:00 - 3:30 Afternoon Tea (Sixth floor) 3:30 - 4:00 Federico Ardila Bergman complexes and Coxeter arrangements. 4:14 - 4:45 Carsten Schultz Cohomology rings of complex projective arrangements. 4:45 - 5:45 Reception (Sixth floor) Wednesday, November 3 9:30 - 10:30 Michel Broue Reductive groups over a field of x elements, x an indeterminate. 10:30 - 11:00 Morning Tea (Sixth floor) 11:00 - 12:00 Alexander Varchenko: The flag variety structure for solutions of the Bethe ansatz equations. 12:15 – 12:45 Laura Stevens Combinatorics of rational functions and PBW expansions of the canonical U(n-)-valued differential form. 12:45 – 5:00 No scheduled talks Thursday, November 4 9:30 - 10:30 Richard Stanley Hyperplane arrangements and special relativity. 10:30 -11:00 Morning Tea (Sixth floor) 11:00 - 12:00 Volkmar Welker Real rootedness and unimodality in discrete geometry. 12:00 - 2:00 Lunch Break 2:00 - 3:00 Alexander Postnikov Hyperplane arrangements and ideals generated by powers of linear forms. 3:00 - 3:30 Afternoon Tea (Sixth floor) 3:30 - 4:00 Patricia Hersh Some remarks on modular elements in lattices. 4:15 - 5:15 Anne Shepler Reflection Groups and Modular Invariant Theory. Friday, November 5 9:30 - 10:30 Christos Athanasiadis Catalan and Narayana numbers for Weyl groups. 10:30 - 11:00 Morning Tea (Sixth floor) 11:00 - 12:00 Hiroaki Terao On the multi-free arrangements. 12:00 - 2:00 Lunch Break 2:00 - 3:00 Alexandru Suciu A look at right-angled Artin groups 3:00 - 3:30 Afternoon Tea (Sixth floor)