Hilbert schemes of points on singular surfaces: combinatorics, geometry, and representation theory
Balazs Szendroi (University of Oxford, UK)
Abstract: Given a smooth algebraic surface S over the complex numbers, the Hilbert scheme of points of S is the starting point for many investigations, leading in particular to generating functions with modular behaviour and Heisenberg algebra representations. I will explain aspects of a similar story for surfaces with rational double points, with links to algebraic combinatorics and the representation theory of affine Lie algebras. I will in particular recall our 2015 conjecture concerning the generating function of the Euler characteristics of the Hilbert scheme for this singular case, and aspects of more recent work that lead to a very recent proof of the conjecture by Nakajima. Joint work with Gyenge and Nemethi, respectively Craw, Gammelgaard and Gyenge.
mathematical physicscommutative algebraalgebraic geometryrings and algebrasrepresentation theorysymplectic geometry
Audience: researchers in the topic
Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)
Series comments: Description: Research webinar series
The LAGOON webinar series was supported as part of the International Centre for Mathematical Sciences (ICMS) and the Isaac Newton Institute for Mathematical Sciences (INI) Online Mathematical Sciences Seminars and is now sponsored by the University of Cologne and the University of Pavia. Please register here to obtain the Zoom link and password for the meetings.
LAGOON will take place online every last Wednesday of the month from 14:00-15:00 (Time Zone Berlin, Rome, Paris).
Videos of the talks can be viewed here.
Video recordings of past talks until April 2022 can still be viewed on the ICMS webpage here.
| Organizers: | Severin Barmeier, Frank Neumann*, Sibylle Schroll* |
| *contact for this listing |