Organizing Committee
Abstract

Schubert calculus is the modern approach to classical problems in enumerative algebraic geometry, specifically on flag varieties and their many generalizations. Crystals are combinatorial tools based on quantum groups which arise in the study of representations of Lie algebras. Whittaker functions are special functions on Lie groups or p-adic groups, for example GL(n,F) where F might be the real or complex numbers, or a p-adic field.

The area of intersection between these three topics is combinatorial representation theory. Common tools such as Demazure operators, the Bruhat partial order, and Macdonald polynomials appear in all three areas. Some connections between these three areas are quite new. This workshop will explore these connections.

Confirmed Speakers & Participants

Workshop Schedule

Monday, March 4, 2013
TimeEventLocationMaterials
9:00 - 9:25Registration11th Floor Collaborative Space 
9:25 - 9:30Welcome - ICERM Director11th Floor Lecture Hall 
9:30 - 10:15The zigzag algebra in higher representation theory. - Anthony Licata, Australian National University11th Floor Lecture Hall
10:30 - 11:00Coffee/Tea Break11th Floor Collaborative Space 
11:00 - 11:45Elliptic and cobordism Schubert calculus - Arun Ram, University of Melbourne11th Floor Lecture Hall
12:00 - 2:45Break for Lunch and Free Time  
1:00 - 2:20Representations of affine Kac-Moody groups over local and global fields (ongoing semester course) - Alexander Braverman, Brown University11th Floor Lecture Hall 
2:45 - 3:30Quantum cohomology of flags and symmetric functions - Jennifer Morse, Drexel University11th Floor Lecture Hall
3:45 - 4:15Coffee/Tea Break11th Floor Collaborative Space 
4:15 - 5:00Rotation of invariant tensors and geometric representation theory - Joel Kamnitzer, University of Toronto11th Floor Lecture Hall
5:15 - 6:30Welcome Reception11th Floor Collaborative Space 
Tuesday, March 5, 2013
TimeEventLocationMaterials
9:00 - 9:45Affine Mirkovic-Vilonen polytopes - Peter Tingley, Massachusetts Institute of Technology11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15Vexillary signed permutations and essential sets for classical-type Schubert varieties - David Anderson, Institute of Pure and Applied Mathematics -IMPA11th Floor Lecture Hall
11:30 - 12:15q-Toda systems and quantum K-theory via quasi-maps spaces. - Alexander Braverman, Brown University11th Floor Lecture Hall
12:30 - 2:45Break for Lunch and Free Time  
2:45 - 3:30Symmetric chain decomposition for cyclic quotients of Boolean algebras and relation to cyclic crystals - Patricia Hersh, North Carolina State University11th Floor Lecture Hall
3:45 - 4:15Coffee/Tea Break11th Floor Collaborative Space 
4:15 - 5:00Open Problem Session11th Floor Lecture Hall 
Wednesday, March 6, 2013
TimeEventLocationMaterials
9:00 - 9:45Some properties of the cominuscule quantum K-theory. - Nicolas Perrin, Heinrich-Heine-Universitat Dusseldorf11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15Nonsymmetric Macdonald polynomials, Kirillov-Reshetikhin crystals, and Demazure characters - Anne Schilling, University of California, Davis11th Floor Lecture Hall
11:30 - 12:15Grothendieck polynomials, and factoring permutations using one Demazure factor too many. - Victor Reiner, University of Minnesota11th Floor Lecture Hall
12:30 - 12:35Group Photo11th Floor Lecture Hall 
1:00 - 2:20Representations of affine Kac-Moody groups over local and global fields (ongoing semester course) - Alexander Braverman, Brown University11th Floor Lecture Hall 
2:45 - 3:30Unique Functionals and Representations of Hecke Algebras - Benjamin Brubaker, Massachusetts Institute of Technology and University of Minnesota11th Floor Lecture Hall
3:35 - 5:00Afternoon open for collaborations and free time  
7:00 - 8:30Poster Session and Dessert Reception11th Floor Lecture Hall and Collaborative Space 
Thursday, March 7, 2013
TimeEventLocationMaterials
9:00 - 9:45Representations of the affine BMW algebra - Monica Vazirani, University of California, Davis11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15q-Rook placements and Jordan forms - Martha Yip, University of Pennsylvania11th Floor Lecture Hall 
11:30 - 12:15q-deformed Whittaker functions and the local Langlands correspondence - Sergey Oblezin, Institute of Theoretical and Experimental Physics11th Floor Lecture Hall
12:30 - 2:45Break for Lunch and Free Time  
2:45 - 3:30Level zero Littelmann paths, Kirillov-Reshetikhin crystals, parabolic quantum Bruhat graph, and Macdonald polynomials. - Mark Shimozono, Virginia Polytechnic Institute and State University11th Floor Lecture Hall
3:45 - 5:00Coffee/Tea Break and afternoon of collaborations11th Floor Collaborative Space 
Friday, March 8, 2013
TimeEventLocationMaterials
9:00 - 9:45Degenerate Whittaker functionals for real reductive groups - Siddhartha Sahi, Rutgers University11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15Equivariant jeu de taquin and eigenvalues of Hermitian matrices - Alexander Yong, University of Illinois at Urbana-Champaign11th Floor Lecture Hall
11:30 - 12:15Schubert calculus and Toda lattices - Thomas Lam, University of Michigan11th Floor Lecture Hall 
12:30 - 2:45Break for Lunch and Free Time  
2:45 - 5:00Afternoon open for collaborations and free time11th Floor Collaborative Space 

Tutorial Week Schedule

Monday, February 25, 2013
TimeEventLocationMaterials
10:15 - 11:15Hunting for interesting WMDS via Dynkin diagram heuristics - Jeffrey Hoffstein, Brown University11th Floor Lecture Hall 
11:30 - 12:30Combinatorial Representation Theory: Alcove-path models and Macdonald polynomials - Arun Ram, University of Melbourne11th Floor Lecture Hall 
1:00 - 2:20Representations of affine Kac-Moody groups over local and global fields (ongoing semester course) - Alexander Braverman, Brown University11th Floor Lecture Hall 
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space 
Tuesday, February 26, 2013
TimeEventLocationMaterials
9:00 - 10:00Professional Development Seminar: Ethics in research I11th Floor Lecture Hall 
1:15 - 2:30Postdoc & Grad Student Seminar I11th Floor Lecture Hall 
2:30 - 3:30Hecke algebras, Kazhdan-Lusztig polynomials, and Soergel Bimodules - Anthony Licata, Australian National University11th Floor Lecture Hall 
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space 
Wednesday, February 27, 2013
TimeEventLocationMaterials
10:15 - 11:15Schubert varieties and Schubert calculus - Sara Billey, University of Washington11th Floor Lecture Hall 
11:30 - 12:30Combinatorial Representation Theory: Alcove-path models and Macdonald polynomials Part 1 - Cristian Lenart, University at Albany, SUNY11th Floor Lecture Hall 
1:00 - 2:20Representations of affine Kac-Moody groups over local and global fields (ongoing semester course) - Alexander Braverman, Brown University11th Floor Lecture Hall 
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space 
4:00 - 5:00Postdoc & Grad Student Seminar II10th Floor Classroom 
Thursday, February 28, 2013
TimeEventLocationMaterials
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space 
Friday, March 1, 2013
TimeEventLocationMaterials
10:15 - 11:15Schubert varieties and Schubert calculus - Arun Ram, University of Melbourne11th Floor Lecture Hall 
11:30 - 12:30Combinatorial Representation Theory: Alcove-path models and Macdonald polynomials Part 2 - Cristian Lenart, University at Albany, SUNY11th Floor Lecture Hall 
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space 
4:00 - 5:00Sage coding sprint and help desk  

Associated Semester Workshops

Lecture Videos

q-deformed Whittaker functions and the local Langlands correspondence

Sergey Oblezin
Institute of Theoretical and Experimental Physics
March 7, 2013

Representations of the affine BMW algebra

Monica Vazirani
University of California, Davis
March 7, 2013

Affine Mirkovic-Vilonen polytopes

Peter Tingley
Massachusetts Institute of Technology
March 5, 2013