Organizers: John Lentfer, Mitsuki Hanada, and Nicolle González.
We will be starting with Mark Haiman's survey article Combinatorics, symmetric functions and Hilbert schemes, and the references therein as needed. We will quickly survey the combinatorial setting and then focus more on understanding the geometry of the Hilbert scheme (Sections 4-6) along with future directions (Section 7).
| Date | Speaker | Topic | Notes |
|---|---|---|---|
| 1/23 | John Lentfer | Organization & Sections 1, 2.1 | Introduction and partitions, tableaux, jeu de taquin, charge and cocharge |
| 1/30 | John Lentfer and Nicolle González | Section 3 excluding 3.4.4 | Standard bases, Hall-Littlewood symmetric functions, plethysm, Macdonald symmetric functions |
| 2/6 | Yuji Okitani | Section 3.4.4 | Springer fibers, cohomology of Springer fibers, computational examples |
| Monday 2/12, 2:00-3:30pm, Evans 959 | Sean Griffin | Springer fibers, Schubert cells, Borel–Moore homology, affine paving, Tanisaki ideals | |
| 2/13 | John Lentfer | Section 4 | n! and (n+1)^(n-1) conjectures, Garsia-Haiman modules, diagonal coinvariants, diagonal harmonics |
| 2/20 | Mitsuki Hanada | Computations and examples for Springer fibers and Garsia-Procesi modules | |
| Thursday 2/22, 10:00-11:30am, Evans 762 | Sean Griffin | Springer fibers in general type, affine Springer fibers | |
| Thursday 2/29, 11:00-12:30pm, Evans 732 | Joe Hlavinka | Section 5.1 | Definitions of the Hilbert scheme and isospectral Hilbert scheme, and main theorem |
| Thursday 3/7, 9:30-11:00am, Evans 961 | Swapnil Garg | Section 5.2 | Categorical quotients, G-Hilbert schemes, Hilbert scheme of S_n-orbits, corollary to main theorem |
| Wednesday 3/13, 10:00-11:30am, Evans 730 | Daigo Ito | Section 5.3 | Crepant resolutions, derived categories, and the theorem of Bridgeland, King and Reid |
| Wednesday 3/20, 10:00-11:30, Evans 1064 | Group Discussion | Review of Sections 5.1-5.3 | |
| Thursday 3/21, 10:00am-11:30am, Evans 732 | Eugene Gorsky | Section 6.1 | |
| 3/26 | No seminar - Spring break | ||
| 4/2 | No seminar | ||
| Monday 4/8, 1:30pm-3:00pm, Evans 736 | Eugene Gorsky | ||
| 4/16 | No seminar | ||
| 4/23 | No seminar | ||
| Monday 4/29, 1:30pm-3:00pm, Evans 939 | Mark Haiman | Section 7 |