SCIENTIFIC PROGRAMS AND ACTIVITIES

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) Supported by NSF grants DMS-0652641, DMS-0652652, DMS-0652668, DMS-0652648 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

OVER VIEW

'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)

CONTRIBUTED TALKS
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>math.ucdavis.edu) and Mike Zabrocki, York
University (zabrocki<at>mathstat.yorku.ca)

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:
- http://www.sagemath.org/doc/tutorial/

An introduction to combinatorics in Sage (draft; in French):
- http://wiki.sagemath.org/combinat?action=AttachFile&do=view&target=sagebook-combinat.pdf

The Python tutorial:
- http://docs.python.org/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

Back to top