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Topics in Combinatorial Representation Theory March 17, 2008 - March 21, 2008
Registration Deadline: March 07, 2008 over 16 years ago
To apply for Funding you must register by: December 17, 2007 over 16 years ago
Parent Program:
Organizers Sergey Fomin, Bernard Leclerc, Vic Reiner (Chair), Monica Vazirani

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Representation theory has often been a key to unlocking problems of enumeration and structure for our favorite combinatorial objects. In the reverse direction, answering many of the central questions of representation theory required development of sophisticated combinatorial techniques and constructions. This interplay, which has only intensified in recent years, will be at the focus of the workshop. Potential topics to be discussed include (the combinatorial aspects of): quiver representations; cluster algebras; Macdonald and LLT polynomials; representation-theoretic techniques in quantum/statistical mechanics; generalized Littlewood-Richardson rules, Schur-positivity, and connections with Schubert calculus; crystal bases and graphs; affine Grassmannians, Mirkovic-Vilonen cycles; dual canonical and semi-canonical bases; Horn and Deligne-Simpson problems; tropical calculus in representation theory. A relatively small number of talks should leave ample time for informal discussions and presentations. INVITED SPEAKERS: Harm Derksen (Univ. of Michigan- Ann Arbor) Philippe Di Francesco (CNRS- Saclay) Mark Haiman (Univ. of California- Berkeley) Joel Kamnitzer (Univ. of California- Berkeley, American Inst. of Math.) Michael Kapovich (Univ. of California- Davis) Rinat Kedem (Univ. of Illinois- Urbana) Thomas Lam (Harvard Univ.) Cristian Lenart (SUNY- Albany) George Lusztig (MIT) Alexander Postnikov (MIT) Arun Ram (Univ. of Wisconsin- Madison, Univ. of Melbourne) Anne Schilling (Univ. of California- Davis) Jan Schroer (Univ. of Bonn) Mark Shimozono (Virginia Tech) David Speyer (Clay Math Inst., MIT) John Stembridge (Univ. of Michigan- Ann Arbor) Anatoly Vershik (Steklov Institute- St. Petersburg) Andrei Zelevinsky (Northeastern Univ.) A block of rooms has been reserved at the Rose Garden Inn. Reservations may be made by calling 1-800-992-9005 OR directly on their website. Click on Corporate at the bottom of the screen and when prompted enter code MATH (this code is not case sensitive). By using this code a new calendar will appear and will show MSRI rate on all room types available. The following Group Code should be entered in the "Comment" field when booking through our Website. Group Code = CGMS57. The cut-off date for reservations is March 2, 2008. A block of rooms has been reserved at the Hotel Durant. Please mention the workshop name and reference the following code when making reservations via phone, fax or e-mail: ER0000. The cut-off date for reservations is February 15, 2008.
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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Mar 17, 2008
09:15 AM - 10:30 AM
  Admissible W-graphs
John Stembridge (University of Michigan)
11:00 AM - 12:00 PM
  Hopf algebras, Towers of Algebras and Dual graded graphs
Thomas Lam
02:00 PM - 03:00 PM
  Restrictions of irreducible representations to Levi subgroups and ideal triangles in Euclidean buildings
Michael Kapovich (University of California, Davis)
04:00 PM - 05:00 PM
  Unipotent classes and special Weyl group representations
George Lusztig
Mar 18, 2008
09:30 AM - 10:30 AM
  Combinatorics of Coxeter elements and cluster algebras of finite type
Andrei Zelevinsky
11:00 AM - 12:00 PM
  Dual semicanonical bases and cluster algebras
Jan Schroeer
02:00 PM - 03:00 PM
  Total positivity, matroids, and clusters
Alexander Postnikov (Massachusetts Institute of Technology)
04:00 PM - 05:00 PM
  Sortable elements -- beyond finite type
David Speyer (University of Michigan)
Mar 19, 2008
09:30 AM - 10:30 AM
  Path models
Arun Ram (University of Melbourne)
11:00 AM - 12:00 PM
  Hall-Littlewood polynomials, alcove walks, and the Macdonald polynomial inv statistic
Cristian-Paul Lenart
Mar 20, 2008
09:30 AM - 10:30 AM
  Schubert Polynomials for the affine Grassmannian of the symplectic group
Anne Schilling (University of California, Davis)
11:00 AM - 12:00 PM
  k-Schur functions via multidegrees of Matrix Affine Schubert Varieties
Mark Shimozono
02:00 PM - 03:00 PM
  LLT polynomials
Mark Haiman
Mar 21, 2008
09:30 AM - 10:30 AM
  The Razumov-Stroganov conjecture: loop gas, alternating sign matrices, plane partitions and orbital varieties
Philippe Di Francesco (University of Illinois at Urbana-Champaign)
11:00 AM - 12:00 PM
  Quantum algebra characters and cluster algebras
Rinat Kedem (University of Illinois at Urbana-Champaign)
02:00 PM - 03:00 PM
  Quivers with Potentials
Harm Derksen
04:00 PM - 05:00 PM
  Some Problems of Asymptotic Representation Theory (ART)
Anatoly Vershik