April 21, 2024

July 7-10, 2010
Affine Schubert Calculus Summer School
to be held at the University of Toronto,
Sanford Fleming Building:
Room 1101 (July 7, 9, 10);
Room 3201 (July 8)

July 12-15, 2010
Affine Schubert Calculus Workshop
to be held at the Fields Institute (map)

Organizing Committee:
Anne Schilling, U.C. Davis and Mike Zabrocki, York University
Registration for Summer School and Workshop
Regular fee $100, students and PDF $50
includes meeting materials and coffee breaks

On-site July 7 & July 15
Schedule Audio & Slides
Summer School Abstracts Suggested Readings
Information for Fields Visitors Housing and Hotels
List of Registered Participants Workshop Abstracts


'Affine Schubert Calculus' refers to an extension of Schubert calculus to affine Grassmannians and affine flag varieties. The new approach to affine Schubert calculus is made possible by the recent discovery of certain explicitly defined symmetric functions called k-Schur functions. The k-Schur functions, which arose in the study of the seemingly unrelated Macdonald theory, were recently shown to be connected to the geometry and topology of the affine Grassmanian.

This event consists of a summer school and workshop to be held at Fields Institute over a nine day period. The period July 7-10 will be dedicated to the summer school, with July 11 as a free day and followed by another 4 days of workshop that will consist of contributed talks. The purpose of the summer school is to highlight some of the major developments of the Affine Schubert Calculus related to k-Schur functions with survey presentations and tutorials. The workshop portion of the event will highlight some recent related research.

The summer school will include the following series of lectures:

* Thomas Lam, affine Stanley symmetric functions
* Luc Lapointe, k-Schur functions
* Mark Shimozono, generalizations to other affine group types
* Jennifer Morse, combinatorics of k-tableaux
* Nicolas Thiery and Jason Bandlow, computational aspects and computer implementation

Second week will be dedicated to more recent research highlighting some of the results related to k-Schur functions discovered in the last 3 year period including positivity of k-Schur functions and representation theoretical models of k-Schur functions.

A tentative list of speakers includes:

Confirmed speakers:

Sami Assaf (MIT)
Jason Bandlow (Pennsylvania)
Elizabeth Beazley (Michigan)
Jonah Blasiak (Chicago)
Michael Ehrig (Bonn)
Ghislain Fourier (Köln)
Stephen Griffeth (Edinburgh)
Joel Kamnitzer (Toronto)
Thomas Lam (Michigan)
Luc Lapointe (Talca)
Changzheng Li (Korea IAS)
Lenny Tevlin (New York)
Nicolas Thiery (Orsay)
Hugh Thomas (New Brunswick)
Peter Tingley (MIT)
Reiho Sakamoto (Tokyo)
Luis Serrano (Michigan)

If you are interested in giving a presentation at this event please contact the organizers. The deadline for submission of contributions is May 15, 2010. Anne Schilling, U.C. Davis (anne<at> and Mike Zabrocki, York
University (zabrocki<at>

Suggested Readings:

(1) Geometry parts of the books
Young tableaux by Fulton
Symmetric functions, Schubert polynomials and degeneracy loci by L. Manivel.

(2) The Sage tutorial:

An introduction to combinatorics in Sage (draft; in French):

The Python tutorial:

Lecture notes available here for Thomas Lam's lecture series

Worksheet for Jason Bandlow's talk on Sage

Additional Information regarding Sage Exercises

Notes for Lenny Tevlin's talk

Final List of Participants:

Full Name University Name
Assaf, Sami Massachusetts Institute of Technology
Bandlow, Jason University of Pennsylvania
Bayegan, Darius McMaster University
Beazley, Elizabeth University of Michigan
Belinschi, Serban University of Saskatchewan
Berg, Chris Fields Institute
Bergeron-Brlek, Anouk York University
Bhargava, Sandeep York University
Blasiak, Jonah University of Chicago
Block, Florian University of Michigan
Cao, Lei Drexel University
Chen, Hongjia University of Alberta
Chen, Zhi York University
Cho, Soojin Ajou University
Cho, Yong Seung Ewha Women's University
Csima, Nora Elizabeth University of Illinois at Urbana-Champaign
Dalal, Avinash Drexel University
Darayon, Chayapa University of Illinois at Urbana-Champaign
Denton, Samuel University of California, Davis
Dewitt, Barry McMaster University
Ehrig, Michael University of Bonn
Foster, John University of Oregon
Fourier, Ghislain Universität zu Köln
Griffeth, Stephen University of Edinburgh
Heilman, Derek Drexel University
Ikeda, Takeshi Okayama University of Science
Kamnitzer, Joel University of Toronto
Krithivasan, Narayanan University of Chicago
Lam, Thomas University of Michigan
Lapointe, Luc Universidad de Talca
Lee, Kyungyong Purdue University
Li, Changzheng Korea Institute for Advanced Study
Li, Huilan Drexel University
Li, Nan Massachusetts Institute of Technology
Lubovsky, Arthur SUNY Albany
Miller, Alexander University of Minnesota
Morse, Jennifer Drexel University
Numata, Yasuhide University of Tokyo
Ohn, Christian Universite de Valenciennes
Pabiniak, Milena Cornell University
Pattanayak, Santosha Chennai Mathematical Institute
Pinto, Maria Elena Universidad de Talca
Pittman-Polletta, Benjamin University of Arizona
Pon, Steven University of California, Davis
Purbhoo, Kevin University of Waterloo
Rupel, David University of Oregon
Sakamoto, Reiho University of Tokyo
Schilling, Anne University of California, Davis
Serrano, Luis UQAM
Shimozono, Mark Virginia Tech
Stapledon, Alan University of British Columbia
Stump, Christian UQAM
Tevlin, Lenny New York University
Thiéry, Nicolas M. Université Paris Sud 11
Thind, Jaimal Queen's University
Thomas, Hugh University of New Brunswick
Tingley, Peter Massachusetts Institute of Technology
Tsanov, Valdemar Queen's University
Yip, Martha University of Wisconsin-Madison
Yoo, Hwanchul Massachusetts Institute of Technology
Yun, Taedong Massachusetts Institute of Technology
Zabrocki, Mike York University

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