Mathematical Sciences Research Institute - Topics in Combinatorial Representation Theory

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.

Follow this link to read about the new U.S. visa requirements

Schedule
Monday March 17, 2008
09:15AM - 10:30AM	John Stembridge	Admissible W-graphs (See Abstract)
10:30AM - 11:00AM	Morning tea
11:00AM - 12:00PM	Thomas Lam	Hopf algebras, Towers of Algebras and Dual graded graphs (See Abstract)
12:00PM - 02:00PM	Lunch
02:00PM - 03:00PM	Michael Kapovich	Restrictions of irreducible representations to Levi subgroups and ideal triangles in Euclidean buildings
03:00PM - 04:00PM	Afternoon tea
04:00PM - 05:00PM	George Lusztig	Unipotent classes and special Weyl group representations (See Abstract)
Tuesday March 18, 2008
09:30AM - 10:30AM	Andrei Zelevinsky	Combinatorics of Coxeter elements and cluster algebras of finite type (See Abstract)
10:30AM - 11:00AM	Morning tea
11:00AM - 12:00PM	Jan Schroeer	Dual semicanonical bases and cluster algebras (See Abstract)
12:00PM - 02:00PM	Lunch
02:00PM - 03:00PM	Alexander Postnikov	Total positivity, matroids, and clusters (See Abstract)
03:00PM - 04:00PM	Afternoon tea
04:00PM - 05:00PM	David Speyer	Sortable elements -- beyond finite type (See Abstract)
Wednesday March 19, 2008
09:30AM - 10:30AM	Arun Ram	Path models (See Abstract)
10:30AM - 11:00AM	Morning tea
11:00AM - 12:00PM	Cristian-Paul Lenart	Hall-Littlewood polynomials, alcove walks, and the Macdonald polynomial inv statistic (See Abstract)
Thursday March 20, 2008
09:30AM - 10:30AM	Anne Schilling	Schubert Polynomials for the affine Grassmannian of the symplectic group (See Abstract)
10:30AM - 11:00AM	Morning tea
11:00AM - 12:00PM	Mark Shimozono	k-Schur functions via multidegrees of Matrix Affine Schubert Varieties (See Abstract)
12:00PM - 02:00PM	Lunch
02:00PM - 03:00PM	Mark Haiman	LLT polynomials (See Abstract)
03:00PM - 03:55PM	Afternoon tea
04:10PM - 05:00PM	Joel Kamnitzer	(UC Berkeley Math Colloquium, 60 Evans) Knot homology, geometric representation theory, and derived categories (See Abstract)
Friday March 21, 2008
09:30AM - 10:30AM	Philippe di Francesco	The Razumov-Stroganov conjecture: loop gas, alternating sign matrices, plane partitions and orbital varieties (See Abstract)
10:30AM - 11:00AM	Morning tea
11:00AM - 12:00PM	Rinat Kedem	Quantum algebra characters and cluster algebras (See Abstract)
12:00PM - 02:00PM	Lunch
02:00PM - 03:00PM	Harm Derksen	Quivers with Potentials
03:00PM - 04:00PM	Afternoon tea
04:00PM - 05:00PM	Anatoly Vershik	Some Problems of Asymptotic Representation Theory (ART) (See Abstract)

Currently Available Videos

John Stembridge , Admissible W-graphs March 17,2008, 09:15 AM to 10:30 AM
Thomas Lam , Hopf algebras, Towers of Algebras and Dual graded graphs March 17,2008, 11:00 AM to 12:00 PM
Michael Kapovich , Restrictions of irreducible representations to Levi subgroups and ideal triangles in Euclidean buildings March 17,2008, 02:00 PM to 03:00 PM
George Lusztig , Unipotent classes and special Weyl group representations March 17,2008, 04:00 PM to 05:00 PM
Andrei Zelevinsky , Combinatorics of Coxeter elements and cluster algebras of finite type March 18,2008, 09:30 AM to 10:30 AM
Jan Schroeer , Dual semicanonical bases and cluster algebras March 18,2008, 11:00 AM to 12:00 PM
Alexander Postnikov , Total positivity, matroids, and clusters March 18,2008, 02:00 PM to 03:00 PM
David Speyer , Sortable elements -- beyond finite type March 18,2008, 04:00 PM to 05:00 PM
Arun Ram , Path models March 19,2008, 09:30 AM to 10:30 AM
Cristian-Paul Lenart , Hall-Littlewood polynomials, alcove walks, and the Macdonald polynomial inv statistic March 19,2008, 11:00 AM to 12:00 PM
Anne Schilling , Schubert Polynomials for the affine Grassmannian of the symplectic group March 20,2008, 09:30 AM to 10:30 AM
Mark Shimozono , k-Schur functions via multidegrees of Matrix Affine Schubert Varieties March 20,2008, 11:00 AM to 12:00 PM
Mark Haiman , LLT polynomials March 20,2008, 02:00 PM to 03:00 PM
Philippe di Francesco , The Razumov-Stroganov conjecture: loop gas, alternating sign matrices, plane partitions and orbital varieties March 21,2008, 09:30 AM to 10:30 AM
Rinat Kedem , Quantum algebra characters and cluster algebras March 21,2008, 11:00 AM to 12:00 PM
Harm Derksen , Quivers with Potentials March 21,2008, 02:00 PM to 03:00 PM
Anatoly Vershik , Some Problems of Asymptotic Representation Theory (ART) March 21,2008, 04:00 PM to 05:00 PM

You can find videos of other workshops and events on our VMath - Streaming Video page.

For more information:
Questions about this workshop should be sent either by email to

408@msri.org

or by regular mail to:

Topics in Combinatorial Representation Theory Mathematical Sciences Research Institute 17 Gauss Way, Berkeley, CA 94720-5070. USA

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Topics in Combinatorial Representation Theory

Follow this link to read about the new U.S. visa requirements

Schedule

Monday March 17, 2008

Tuesday March 18, 2008

Wednesday March 19, 2008

Thursday March 20, 2008

Friday March 21, 2008

Currently Available Videos