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.

Image for "Whittaker Functions, Schubert calculus and Crystals"

Confirmed Speakers & Participants

Talks will be presented virtually or in-person as indicated in the schedule below.

  • Speaker
  • Poster Presenter
  • Attendee
  • Virtual Attendee

Workshop Schedule

Monday, March 4, 2013
TimeEventLocationMaterials
9:00 - 9:25am ESTRegistration11th Floor Collaborative Space 
9:25 - 9:30am ESTWelcome - ICERM Director11th Floor Lecture Hall 
9:30 - 10:15am ESTThe zigzag algebra in higher representation theory. - Anthony Licata, Australian National University11th Floor Lecture Hall
10:30 - 11:00am ESTCoffee/Tea Break11th Floor Collaborative Space 
11:00 - 11:45am ESTElliptic and cobordism Schubert calculus - Arun Ram, University of Melbourne11th Floor Lecture Hall
12:00 - 2:45pm ESTBreak for Lunch and Free Time  
1:00 - 2:20pm ESTRepresentations of affine Kac-Moody groups over local and global fields (ongoing semester course) - Alexander Braverman, Brown University11th Floor Lecture Hall 
2:45 - 3:30pm ESTQuantum cohomology of flags and symmetric functions - Jennifer Morse, Drexel University11th Floor Lecture Hall
3:45 - 4:15pm ESTCoffee/Tea Break11th Floor Collaborative Space 
4:15 - 5:00pm ESTRotation of invariant tensors and geometric representation theory - Joel Kamnitzer, University of Toronto11th Floor Lecture Hall
5:15 - 6:30pm ESTWelcome Reception11th Floor Collaborative Space 
Tuesday, March 5, 2013
TimeEventLocationMaterials
9:00 - 9:45am ESTAffine Mirkovic-Vilonen polytopes - Peter Tingley, Massachusetts Institute of Technology11th Floor Lecture Hall
10:00 - 10:30am ESTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15am ESTVexillary signed permutations and essential sets for classical-type Schubert varieties - David Anderson, Institute of Pure and Applied Mathematics -IMPA11th Floor Lecture Hall
11:30 - 12:15pm ESTq-Toda systems and quantum K-theory via quasi-maps spaces. - Alexander Braverman, Brown University11th Floor Lecture Hall
12:30 - 2:45pm ESTBreak for Lunch and Free Time  
2:45 - 3:30pm ESTSymmetric chain decomposition for cyclic quotients of Boolean algebras and relation to cyclic crystals - Patricia Hersh, North Carolina State University11th Floor Lecture Hall
3:45 - 4:15pm ESTCoffee/Tea Break11th Floor Collaborative Space 
4:15 - 5:00pm ESTOpen Problem Session11th Floor Lecture Hall 
Wednesday, March 6, 2013
TimeEventLocationMaterials
9:00 - 9:45am ESTSome properties of the cominuscule quantum K-theory. - Nicolas Perrin, Heinrich-Heine-Universitat Dusseldorf11th Floor Lecture Hall
10:00 - 10:30am ESTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15am ESTNonsymmetric Macdonald polynomials, Kirillov-Reshetikhin crystals, and Demazure characters - Anne Schilling, University of California, Davis11th Floor Lecture Hall
11:30 - 12:15pm ESTGrothendieck polynomials, and factoring permutations using one Demazure factor too many. - Victor Reiner, University of Minnesota11th Floor Lecture Hall
12:30 - 12:35pm ESTGroup Photo11th Floor Lecture Hall 
1:00 - 2:20pm ESTRepresentations of affine Kac-Moody groups over local and global fields (ongoing semester course) - Alexander Braverman, Brown University11th Floor Lecture Hall 
2:45 - 3:30pm ESTUnique Functionals and Representations of Hecke Algebras - Benjamin Brubaker, Massachusetts Institute of Technology and University of Minnesota11th Floor Lecture Hall
3:35 - 5:00pm ESTAfternoon open for collaborations and free time  
7:00 - 8:30pm ESTPoster Session and Dessert Reception11th Floor Lecture Hall and Collaborative Space 
Thursday, March 7, 2013
TimeEventLocationMaterials
9:00 - 9:45am ESTRepresentations of the affine BMW algebra - Monica Vazirani, University of California, Davis11th Floor Lecture Hall
10:00 - 10:30am ESTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15am ESTq-Rook placements and Jordan forms - Martha Yip, University of Pennsylvania11th Floor Lecture Hall 
11:30 - 12:15pm ESTq-deformed Whittaker functions and the local Langlands correspondence - Sergey Oblezin, Institute of Theoretical and Experimental Physics11th Floor Lecture Hall
12:30 - 2:45pm ESTBreak for Lunch and Free Time  
2:45 - 3:30pm ESTLevel 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 - 5:00pm ESTCoffee/Tea Break and afternoon of collaborations11th Floor Collaborative Space 
Friday, March 8, 2013
TimeEventLocationMaterials
9:00 - 9:45am ESTDegenerate Whittaker functionals for real reductive groups - Siddhartha Sahi, Rutgers University11th Floor Lecture Hall
10:00 - 10:30am ESTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15am ESTEquivariant jeu de taquin and eigenvalues of Hermitian matrices - Alexander Yong, University of Illinois at Urbana-Champaign11th Floor Lecture Hall
11:30 - 12:15pm ESTSchubert calculus and Toda lattices - Thomas Lam, University of Michigan11th Floor Lecture Hall 
12:30 - 2:45pm ESTBreak for Lunch and Free Time  
2:45 - 5:00pm ESTAfternoon open for collaborations and free time11th Floor Collaborative Space 

Tutorial Week Schedule

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

Associated Semester Workshops

Lecture Videos

Schubert calculus and Toda lattices

Thomas Lam
University of Michigan
March 8, 2013
Whittaker Functions, Schubert calculus and Crystals
Play

Equivariant jeu de taquin and eigenvalues of Hermitian matrices

Alexander Yong
University of Illinois at Urbana-Champaign
March 8, 2013
Whittaker Functions, Schubert calculus and Crystals
Play     Abstract

Degenerate Whittaker functionals for real reductive groups

Siddhartha Sahi
Rutgers University
March 8, 2013
Whittaker Functions, Schubert calculus and Crystals
Play     Abstract     Slides

q-deformed Whittaker functions and the local Langlands correspondence

Sergey Oblezin
Institute for Theoretical and Experimental Physics
March 7, 2013
Whittaker Functions, Schubert calculus and Crystals
Play     Abstract     Slides

q-Rook placements and Jordan forms

Martha Yip
University of Pennsylvania
March 7, 2013
Whittaker Functions, Schubert calculus and Crystals
Play

Representations of the affine BMW algebra

Monica Vazirani
University of California, Davis
March 7, 2013
Whittaker Functions, Schubert calculus and Crystals
Play     Abstract     Slides

Grothendieck polynomials, and factoring permutations using one Demazure factor too many.

Victor Reiner
University of Minnesota
March 6, 2013
Whittaker Functions, Schubert calculus and Crystals
Play     Abstract

Nonsymmetric Macdonald polynomials, Kirillov-Reshetikhin crystals, and Demazure characters

Anne Schilling
UC Davis
March 6, 2013
Whittaker Functions, Schubert calculus and Crystals
Play     Abstract

Some properties of the cominuscule quantum K-theory.

Nicolas Perrin
Heinrich-Heine-Universität Düsseldorf
March 6, 2013
Whittaker Functions, Schubert calculus and Crystals
Play     Abstract

Symmetric chain decomposition for cyclic quotients of Boolean algebras and relation to cyclic crystals

Patricia Hersh
North Carolina State University
March 5, 2013
Whittaker Functions, Schubert calculus and Crystals
Play     Abstract

Vexillary signed permutations and essential sets for classical-type Schubert varieties

David Anderson
Institute of Pure and Applied Mathematics (IMPA)
March 5, 2013
Whittaker Functions, Schubert calculus and Crystals
Play     Abstract     Slides

Affine Mirkovic-Vilonen polytopes

Peter Tingley
Loyola University
March 5, 2013
Whittaker Functions, Schubert calculus and Crystals
Play     Abstract     Slides

Rotation of invariant tensors and geometric representation theory

Joel Kamnitzer
University of Toronto
March 4, 2013
Whittaker Functions, Schubert calculus and Crystals
Play     Abstract

Elliptic and cobordism Schubert calculus

Arun Ram
University of Melbourne
March 4, 2013
Whittaker Functions, Schubert calculus and Crystals
Play     Abstract     Slides

The zigzag algebra in higher representation theory.

Anthony Licata
Australian National University
March 4, 2013
Whittaker Functions, Schubert calculus and Crystals
Play     Abstract