Home /  Combinatorial Aspects of Hyperplane Arrangements


Combinatorial Aspects of Hyperplane Arrangements November 01, 2004 - November 05, 2004
Registration Deadline: November 05, 2004 over 19 years ago
To apply for Funding you must register by: August 01, 2004 almost 20 years ago
Parent Program:
Organizers Eva Maria Feichtner, Philip Hanlon, Peter Orlik, Alexander Varchenko

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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)
Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
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To apply for funding, you must register by the funding application deadline displayed above.

Students, recent PhDs, women, and members of underrepresented minorities are particularly encouraged to apply. Funding awards are typically made 6 weeks before the workshop begins. Requests received after the funding deadline are considered only if additional funds become available.

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For information about recommended hotels for visits of under 30 days, visit Short-Term Housing. Questions? Contact coord@slmath.org.

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Schedule, Notes/Handouts & Videos
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Nov 01, 2004
09:30 AM - 10:30 AM
  Hyperplane Face Semigroups and their Algebras.
Ken Brown (University of Glasgow)
11:00 AM - 12:00 PM
  Are there Q-deformations of Hyperplanes that are Useful for Shuffling?
Persi Diaconis (Stanford University)
Nov 02, 2004
08:10 AM - 09:10 AM
  Introduction to Matroid Polytopes.
Bernd Sturmfels (University of California, Berkeley; Max-Planck-Institut für Mathematik in den Naturwissenschaften)
09:30 AM - 10:30 AM
  Nested Set Complexes in Geometric Combinatorics.
Eva Feichtner (Universität Bremen)
11:00 AM - 12:00 PM
  Combinatorics of DeConcini-Procesi Resolutions ofthe Real Permutation Action.
Dmitry Feichtner-Kozlov
02:00 PM - 03:00 PM
  Combinatorial Stratifications of the Grassmanians: Algebraic Geometry and Combinatorial Fiber Bundles.
Nicoli Mnev
03:30 PM - 04:00 PM
  Bergman Complexes and Coxeter Arrangements.
Federico Ardila (San Francisco State University)
04:15 PM - 04:45 PM
  Cohomology Rings of Complex Projective Arrangements.
Carsten Schultz
Nov 03, 2004
09:30 AM - 10:30 AM
  Reductive Groups Over a Field of X Elements, X an Indeterminate
Michel Broué (Institut de Mathematiques de Jussieu)
11:00 AM - 12:00 PM
  The Flag Variety Structure for Solutions of the Bethe Ansatz Equations.
Alexander Varchenko (University of North Carolina)
12:15 PM - 12:45 PM
  Combinatorics of Rational Functions and PBW Expansions of the Canonical U(n_)-valued Differential Form.
Laura Stevens
Nov 04, 2004
09:30 AM - 10:30 AM
  Hyperplane Arrangements and Special Relativity.
Richard Stanley (University of Miami)
11:00 AM - 12:00 PM
  Real Rootedness and Unimodality in Discrete Geometry.
Volkmar Welker (Philipps-Universität Marburg)
02:00 PM - 03:00 PM
  Hyperplane Arrangements and Ideals Generated by Powers of Linear Forms.
Alexander Postnikov (Massachusetts Institute of Technology)
03:30 PM - 04:00 PM
  Some Remarks on Modular Elements in Lattices.
Patricia Hersh (North Carolina State University)
04:15 PM - 05:15 PM
  Reflection Groups and Modular Invariants Theory.
Anne Shepler (University of North Texas)
Nov 05, 2004
09:30 AM - 10:30 AM
  Catalan and Narayana Numbers for Weyl Groups.
Christos Athanasiadis
02:00 PM - 03:00 PM
  On the Multi-Free Arrangements.
Hiroaki Terao (Hokkaido University)
02:00 PM - 03:00 PM
  A Look at Right-Angled Artin Groups.
Alexandru Suciu (Northeastern University)