Macdonald Polynomials and Geometry
March 8 - 11, 2010
The goal of this worshop was to gather experts from various backgrounds with an interest in Macdonald polynomials and their connection to geometry.
The Macdonald polynomials, since their inception in the late 80's, have proved to be crucial to a number of questions in combinatorics with a tight connection to algebraic geometry and representation theory. The main aim of the workshop was to give the opportunity for researchers in these areas (combinatorics, algebraic geometry, representation theory) to share their knowledge and points of view on the subject. The hope is to increase our understanding of the Macdonald polynomials and the central role they play in Mathematics by focusing in their various remarkable geometric incarnations.
Some of the work connecting Macdonald polynomials and geometry are the following: Haiman on the geometry of the Hilbert schemes; Schiffmann and Vasserot on Macdonald polynomials and the Hall algebras of elliptic curves; Hausel, Letellier and Rodriguez Villegas on the geometry of certain character and quiver varieties.
The workshop was held at the Clay Mathematics Institute Headquarters in Cambridge, Massachusetts.
Schedule
Monday, March 8
| 9:30-10:30 | Registration |
| 10:30-12:00 | Fernando Rodriguez-Villegas, Counting points of character varieties over finite fields |
| 12:00-2:00 | Lunch |
| 2:00-3:30 | Daniel Juteau, Parity Sheaves |
| 4:00-5:30 | Emmanuel Letellier, Intersection cohomology on character/quiver varieties and the character ring of finite general linear groups |
Tuesday, March 9
| 10:00-11:30 | Olivier Schiffmann, Hall algebras of curves and Langlands duality |
| 11:30-1:30 | Lunch |
| 2:00-3:30 | Alexander Tsymbaliuk, Gelfand-Tsetlin bases via Laumon spaces |
| 4:00-5:30 | Nagao Kentaro, Vertex operators in Donaldson-Thomas theory |
Wednesday, March 10
| 10:00-11:30 | Alexi Oblomkov, Quamtum cohomology of the Hilbert scheme points on An-resolution |
| 11:30-1:30 | Lunch |
| 2:00-3:30 | David Ben-Zvi, The character topological field theory |
| 4:00-5:30 | Pavel Etingof, Supports of irreducible spherical representations of rational Cherednik algebras of finite Coxeter groups |
| 10:00-11:30 | Mark Shimozono, k-shape functions and cohomology of the affine Grassmannian | 12:00-1:30 | David Nadler, Geometry of character sheaves |
| 2:00-5:00 | Closing Luncheon |
Organizers
- David Ellwood (CMI)
- Emmanuel Letellier (University of Caen)
- Olivier Schiffmann (Jussieu University)
- Fernando Rodriguez Villegas (UT Austin)
Participants
- David Ben-Zvi (UT Austin)
- David Nadler (Northwestern Uiversity)
- Pavel Etingof (MIT)
- Daniel Juteau (University of Caen)
- Nagao Kentaro (RIMS Kyoto University)
- Alexi Oblomkov (Princeton University)
- Mark Shimozono (Virginia Tech)
- Alexander Tsymbaliuk (MIT)
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