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Whittaker Functions, Schubert calculus and Crystals (March 4-8, 2013)


Organizing Committee
Description

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.


  • Bogdan Ion
    (University of Pittsburgh)
  • Nicolas Jacon
    (Université de Franche-Comté (Besançon))
  • Garrett Johnson
    (Catholic University of America)
  • Brant Jones
    (James Madison University)
  • Michael Joyce
    (Tulane University)
  • Joel Kamnitzer*
    (University of Toronto)
  • Hyosang Kang
    (Korea Institute for Advanced Study (KIAS))
  • Cihan Karabulut
    (City University of New York (CUNY))
  • Henry Kim
    (University of Toronto)
  • Yeansu Kim
    (Purdue University)
  • Eren Kiral
    (Brown University)
  • Chan Ieong Kuan
    (Brown University)
  • Deniz Kus
    (Universität zu Köln)
  • Thomas Lam*
    (University of Michigan)
  • Martina Lanini
    (University of Melbourne)
  • Cedric Lecouvey
    (Université de Tours (François Rabelais))
  • Kyu-Hwan Lee
    (University of Connecticut)
  • Min Lee
    (Brown University)
  • Cristian Lenart
    (University at Albany (SUNY))
  • Nan Li
    (MIT)
  • Winnie Li
    (Pennsylvania State University)
  • Anthony Licata *
    (Australian National University)
  • Li-Mei Lim
    (Brown University)
  • David Lowry
    (Brown University)
  • Arthur Lubovsky
    (University at Albany (SUNY))
  • Xiaoguang Ma
    (University of Illinois at Urbana-Champaign)
  • Peter McNamara
    (Stanford University)
  • Leonardo Mihalcea
    (Virginia Polytechnic Institute and State University)
  • Alejandro Morales
    (University of Quebec)
  • Jennifer Morse *
    (Drexel University)
  • Dinakar Muthiah
    (Brown University)
  • Satoshi Naito
    (Tokyo Institute of Technology)
  • Maki Nakasuji
    (Kitasato University)
  • Sergey Oblezin*
    (Institute of Theoretical and Experimental Physics)
  • Soichi Okada
    (Nagoya University)
  • Omar Ortiz
    (University of Melbourne)
  • Yoon Kyung Park
    (Korea Institute for Advanced Study (KIAS))
  • Manish Patnaik
    (Yale University)
  • Oliver Pechenik
    (University of Illinois at Urbana-Champaign)
  • Nicolas Perrin *
    (Heinrich-Heine-Universität Düsseldorf)
  • Anna Puskas
    (Columbia University)
  • Arun Ram *
    (University of Melbourne)
  • Kevin Ramer
    (University at Albany (SUNY))
  • Vic Reiner *
    (University of Minnesota)
  • Edward Richmond
    (University of British Columbia)
  • Daisuke Sagaki
    (University of Tsukuba)
  • Siddhartha Sahi *
    (Rutgers University)
  • Yiannis Sakellaridis
    (Rutgers University)
  • Ben Salisbury
    (City College, CUNY)
  • Anne Schilling *
    (University of California, Davis)
  • Travis Scrimshaw
    (University of California, Davis)
  • Dominic Searles
    (University of Illinois at Urbana-Champaign)
  • Anastasia Shabanskaya
    (Eastern Connecticut State University)
  • Xin Shen
    (University of Minnesota)
  • Mark Shimozono*
    (Virginia Polytechnic Institute and State University)
  • Jessica Striker
    (University of Minnesota)
  • Christian Stump
    (Universität Hannover)
  • Kaisa Taipale
    (Cornell University)
  • Nicolas Thiery
    (Université de Paris XI (Paris-Sud))
  • Ruoguang (Roger) Tian
    (University of California, Davis)
  • Miguel Tierz
    (Universidad Complutense de Madrid)
  • Peter Tingley *
    (Massachusetts Institute of Technology)
  • Wuttisak Trongsiriwat
    (Massachusetts Institute of Technology)
  • Bart Van Steirteghem
    (Medgar Evers College - CUNY)
  • Monica Vazirani *
    (University of California, Davis)
  • Vidya Venkateswaran
    (Massachusetts Institute of Technology)
  • Christopher Vinroot
    (College of William and Mary)
  • Aladin Virmaux
    (Université de Paris XI (Paris-Sud))
  • Jun Wen
    (Stony Brook University)
  • Ian Whitehead
    (Columbia University)
  • Siman Wong
    (University of Massachusetts)
  • Oded Yacobi
    (University of Toronto)
  • Martha Yip *
    (University of Pennsylvania)
  • Alexander Yong *
    (University of Illinois at Urbana-Champaign)
  • Hwanchul Yoo
    (KIAS)
  • Meesue Yoo
    (Korea Institute for Advanced Study (KIAS))
  • Qiao Zhang
    (Texas Christian University)
DatesTitleOrganizers
March 4-8, 2013Whittaker Functions, Schubert calculus and CrystalsSara Billey, Daniel Bump, Cristian Lenart

Tutorial Video Links
Description Speaker
Video
Abstract
Slides


Workshop Video Links
Description Speaker
Video
Abstract
Slides
MondayFebruary 25, 2013
TimeDescriptionSpeakerLocationAbstractsSlides
10:15 - 11:15Hunting for interesting WMDS via Dynkin diagram heuristicsJeffrey Hoffstein, Brown University11th Floor Lecture Hall
11:30 - 12:30Combinatorial Representation Theory: Alcove-path models and Macdonald polynomialsArun Ram, University of Melbourne11th Floor Lecture Hall
PDF
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

TuesdayFebruary 26, 2013
TimeDescriptionSpeakerLocationAbstractsSlides
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 BimodulesAnthony Licata, Australian National University11th Floor Lecture Hall
PDF
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space

WednesdayFebruary 27, 2013
TimeDescriptionSpeakerLocationAbstractsSlides
10:15 - 11:15Schubert varieties and Schubert calculusSara Billey, University of Washington11th Floor Lecture Hall
PDF
11:30 - 12:30Combinatorial Representation Theory: Alcove-path models and Macdonald polynomials Part 1Cristian Lenart, University at Albany, SUNY11th Floor Lecture Hall
PDF
PDF
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

ThursdayFebruary 28, 2013
TimeDescriptionSpeakerLocationAbstractsSlides
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space

FridayMarch 1, 2013
TimeDescriptionSpeakerLocationAbstractsSlides
10:15 - 11:15Schubert varieties and Schubert calculusArun Ram, University of Melbourne11th Floor Lecture Hall
PDF
11:30 - 12:30Combinatorial Representation Theory: Alcove-path models and Macdonald polynomials Part 2Cristian Lenart, University at Albany, SUNY11th Floor Lecture Hall
PDF
PDF
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space
4:00 - 5:00Sage coding sprint and help desk

MondayMarch 4, 2013
TimeDescriptionSpeakerLocationAbstractsSlides
9:00 - 9:25Registration11th Floor Collaborative Space
9:25 - 9:30WelcomeICERM Director11th Floor Lecture Hall
9:30 - 10:15The zigzag algebra in higher representation theory.Anthony Licata, Australian National University11th Floor Lecture Hall
PDF
10:30 - 11:00Coffee/Tea Break11th Floor Collaborative Space
11:00 - 11:45Elliptic and cobordism Schubert calculusArun Ram, University of Melbourne11th Floor Lecture Hall
PDF
PDF
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 functionsJennifer Morse, Drexel University11th Floor Lecture Hall
PDF
3:45 - 4:15Coffee/Tea Break11th Floor Collaborative Space
4:15 - 5:00Rotation of invariant tensors and geometric representation theoryJoel Kamnitzer, University of Toronto11th Floor Lecture Hall
PDF
5:15 - 6:30Welcome Reception11th Floor Collaborative Space

TuesdayMarch 5, 2013
TimeDescriptionSpeakerLocationAbstractsSlides
9:00 - 9:45Affine Mirkovic-Vilonen polytopesPeter Tingley, Massachusetts Institute of Technology11th Floor Lecture Hall
PDF
PDF
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space
10:30 - 11:15Vexillary signed permutations and essential sets for classical-type Schubert varietiesDavid Anderson, Institute of Pure and Applied Mathematics -IMPA11th Floor Lecture Hall
PDF
PDF
11:30 - 12:15q-Toda systems and quantum K-theory via quasi-maps spaces.Alexander Braverman, Brown University11th Floor Lecture Hall
PDF
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 crystalsPatricia Hersh, North Carolina State University11th Floor Lecture Hall
PDF
3:45 - 4:15Coffee/Tea Break11th Floor Collaborative Space
4:15 - 5:00Open Problem Session11th Floor Lecture Hall

WednesdayMarch 6, 2013
TimeDescriptionSpeakerLocationAbstractsSlides
9:00 - 9:45Some properties of the cominuscule quantum K-theory.Nicolas Perrin, Heinrich-Heine-Universitat Dusseldorf11th Floor Lecture Hall
PDF
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space
10:30 - 11:15Nonsymmetric Macdonald polynomials, Kirillov-Reshetikhin crystals, and Demazure charactersAnne Schilling, University of California, Davis11th Floor Lecture Hall
PDF
11:30 - 12:15Grothendieck polynomials, and factoring permutations using one Demazure factor too many.Victor Reiner, University of Minnesota11th Floor Lecture Hall
PDF
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 AlgebrasBenjamin Brubaker, Massachusetts Institute of Technology and University of Minnesota11th Floor Lecture Hall
PDF
3:35 - 5:00Afternoon open for collaborations and free time
7:00 - 8:30Poster Session and Dessert Reception11th Floor Lecture Hall and Collaborative Space

ThursdayMarch 7, 2013
TimeDescriptionSpeakerLocationAbstractsSlides
9:00 - 9:45Representations of the affine BMW algebraMonica Vazirani, University of California, Davis11th Floor Lecture Hall
PDF
PDF
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space
10:30 - 11:15q-Rook placements and Jordan formsMartha Yip, University of Pennsylvania11th Floor Lecture Hall
11:30 - 12:15q-deformed Whittaker functions and the local Langlands correspondenceSergey Oblezin, Institute of Theoretical and Experimental Physics11th Floor Lecture Hall
PDF
PDF
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
PDF
3:45 - 5:00Coffee/Tea Break and afternoon of collaborations11th Floor Collaborative Space

FridayMarch 8, 2013
TimeDescriptionSpeakerLocationAbstractsSlides
9:00 - 9:45Degenerate Whittaker functionals for real reductive groupsSiddhartha Sahi, Rutgers University11th Floor Lecture Hall
PDF
PDF
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space
10:30 - 11:15Equivariant jeu de taquin and eigenvalues of Hermitian matricesAlexander Yong, University of Illinois at Urbana-Champaign11th Floor Lecture Hall
PDF
11:30 - 12:15Schubert calculus and Toda latticesThomas 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