| Speaker: | Dmytro Matvieievskyi (University of Massachusetts, Amherst) |
|---|---|
| Title: | Counting leaves on symplectic dual varieties: nilpotent cones |
| Date (JST): | Thu, Dec 18, 2025, 13:30 - 15:00 |
| Place: | Seminar Room B |
| Abstract: |
Roughly speaking, symplectic duality connects pairs of conical symplectic singularities that share or interchange certain geometric data and are expected to satisfy many interesting properties with regard to each other. One of such expectations is a relation between stratifications by symplectic leaves, for Higgs and Coulomb branches it is expected to have a bijection on the set of symplectic leaves. Looking at the main example of my talk (nilpotent cones for simple Lie group G and its Langlands dual G^\vee), we can easily see that the number of symplectic leaves is different. I will try to explain how to remedy this issue by considering certain covers of symplectic leaves and providing a bijection between them, which is a geometric interpretation of Achar duality and related to dualities of Sommers and Barbasch-Vogan-Lusztig-Spaltenstein. Time permitting, I will talk a bit on what to expect for more general symplectic dual pairs. |
