Workshop on Schubert Varieties and Schubert Calculus
Description
The topics of Schubert varieties and the intersection theory of Schubert calculus are at the crossroads of algebraic geometry, representation theory, symplectic geometry and combinatorics. The goal of this workshop is to introduce some of the themes of research in this subject through expository lectures and discussion sessions, as well as through research talks. In particular, we hope to facilitate interaction between mathematicians (including graduate students) in Toronto and the southern Ontario area.
A series of expository lectures will focus on:
1. Schubert varieties
2. Smoothness of Schubert varieties
3. Positivity problems in Schubert calculus
4. Borel's theorem and Schubert polynomials
5. Equivariant cohomology of flag varieties
6. Quantum cohomology of flag varieties
7. K-theory of flag varieties
8. Intersection theory of degeneracy loci
There is no registration fee but those planning to attend are asked to contact Alexander Yong at ayong@fields.utoronto.ca.
Current Speakers/Participants:
|
Dave Anderson (Michigan) |
Augustin-Liviu Mare (Regina) |
Schedule
| 09:00 to 09:30 |
Morning Coffee
|
| 09:30 to 10:30 |
Schubert calculus: algebraic geometry and combinatorics
Alexander Yong, University of Illinois at Urbana-Champagin |
| 10:30 to 11:00 |
Coffee Break
|
| 11:00 to 12:00 |
Schubert basics
Megumi Harada, McMaster University |
| 12:00 to 14:00 |
Lunch Break
|
| 14:00 to 15:00 |
Cohomology of flag varieties
Alistair Savage, University of Ottawa |
| 15:00 to 15:30 |
Coffee Break
|
| 15:30 to 16:30 |
Mirkovic-Vilonen cycles
Joel Kamnitzer, University of Toronto |
| 09:00 to 09:30 |
Morning Coffee
|
| 09:30 to 10:30 |
Quantum cohomology of full flag manifolds I. Generators and relations
Augustin Liviu-Mare, University of Regina |
| 10:30 to 11:00 |
Coffee Break
|
| 11:00 to 12:00 |
Schubert polynomials
Nantel Bergeron, York University |
| 12:00 to 14:00 |
Lunch Break
|
| 14:00 to 15:00 |
Degeneracy loci
Alexander Yong, University of Illinois at Urbana-Champagin |
| 15:00 to 15:30 |
Coffee Break
|
| 15:30 to 16:30 |
Quantum cohomology of full flag manifolds II. The quantum Chevalley formula
Augustin Liviu-Mare, University of Regina |
| 09:00 to 09:30 |
Morning Coffee
|
| 09:30 to 10:30 |
Equivariant cohomology
Linda Chen, The Ohio State University |
| 10:30 to 11:00 |
Coffee Break
|
| 11:00 to 12:00 |
K-theory
Mathieu Willems, University of Toronto |
| 12:00 to 14:00 |
Lunch Break
|
| 14:00 to 15:00 |
Equivariant cohomology and GKM theory for flag varieties
Megumi Harada, McMaster University |
| 15:00 to 15:30 |
Coffee Break
|
| 15:30 to 16:30 |
Equivariant K-theory of Bott-Samelson varieties and flag varieties
Mathieu Willems, University of Toronto |
| 09:00 to 09:30 |
Morning Coffee
|
| 09:30 to 10:30 |
Introduction to the Singularities of Schubert Varieties
Alexander Woo, University of Idaho |
| 10:30 to 11:00 |
Coffee Break
|
| 11:00 to 12:00 |
Geometric representation theory on flag varieties
Alistair Savage, University of Ottawa |
| 12:00 to 14:00 |
Lunch Break
|
| 14:00 to 15:00 |
Some comments about varieties defined by rank conditions
Brian Rothbach, University of California Berkeley |
| 15:00 to 15:30 |
Coffee Break
|
| 15:30 to 16:30 |
Equivariant quantum Schubert calculus
Leonardo Mihalcea, Virginia Tech |
| 09:00 to 09:30 |
Morning Coffee
|
| 09:30 to 10:30 |
Regular semisimple Hessenberg varieties
Julianna Tymoczko, Smith College |
| 10:30 to 11:00 |
Coffee Break
|
| 11:00 to 12:00 |
Geometric realizations of quantum cohomology of SL_n/P
Konstanze Rietsch, King's College London |
