Quantum/Affine Schubert Calculus

5 August - 9 August 2013
University of Oregon
Eugene, OR

The goal of this workshop will be to understand the ring isomorphism (after localization) between the quantum cohomology of the flag variety and the homology ring of the affine Grassmannian. This result was asserted in unpublished notes by Dale Peterson, and later formalized and proven by Thomas Lam and Mark Shimozono in the following paper:

Quantum cohomology of G/P and homology of affine Grassmannian.

Along the way, we will learn about Schubert calculus, equivariant cohomology, quantum cohomology, the affine Grassmannian, and the Toda lattice, with an emphasis on concrete examples and computations.

The workshop will be led by Allen Knutson.


Here is a preliminary schedule of talks.

Practical information

Participants will be staying in the Carson residence hall on campus. When you arrive on Sunday, you need to check in at the Area Desk of the Living Learning Center, which is on 15th Avenue between University Street and Agate Street; there you will receive a key to your room. The confusing thing is that the building is disconnected (there is a South component and a North component). The component on 15th Avenue is the South component, but the component that contains the Area Desk is the North component (which is not bordered by any street at all). Also, if you arrive after 8pm, you will have to call this number: (541) 346-5686.

There is no public transportation from the airport, so you'll have to take a cab, which should take about half an hour and cost about $30. Since a lot of you will be arriving around the same time, you might consider trying to find each other at the airport and sharing a cab. To help coordinate this, you can use this page.

If you are planning to drive to Eugene, I can get you a parking pass; please contact me directly.

Here are a few suggestions for where to eat.


This is the fourth of a series of summer workshops that have been funded by an NSF CAREER grant. You can read about the previous ones here:

2010: Operator Algebras and Conformal Field Theory (with André Henriques)
2011: Cluster Algebras and Lusztig's Semicanonical Basis (with David Speyer)
2012: Categorical Representation Theory (with David Ben-Zvi)


If you are interested in participating, email me. Please include your school, advisor, and a brief description of your research interests. Funding for accommodations in Eugene (but not for travel) will be available to students and postdocs as long as space remains.