Graduate Workshop on Geometry of Hilbert schemes: November 18 – 22, 2013

Organized by Mark de Cataldo, Alexander Kirillov, Jr., and Robert Lazarsfeld.

Dates: November 18 – 22, 2013

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Given a smooth algebraic surface X, the collection of all n-tuples of points on X (or, more precisely, finite subschemes of X of length n) are parametrized by the punctual Hilbert scheme of X. Over the past two decades. these remarkable parameter spaces have come up in a surprisingly wide range of mathematical areas ranging from algebraic geometry to representation theory to combinatorics. This workshop will expose graduate students to the geometry of these Hilbert schemes, as well as some of the questions to which they have been applied. In addition to basic theory, the workshop will also cover topics such as  computation of cohomology of Hilbert schemes, relation to McKay correspondence and representations of Heisenberg and affine Lie algebras, hyperkahler geometry and the n! conjecture.

The lectures on the basic theory, computation of cohomology and relations to representation theory will be given by Robert Lazarsfeld,  Mark Andrea de Cataldo and Alexander Kirillov Jr., respectively. The ones on more advanced topics will be given by outside experts, including Izzet Coskun. We expect that some single-topic lectures will be given by the graduate participants in the workshop. There will also be a daily discussion session.

Please note that this workshop is partially funded by the National Science Foundation.  In addition to the acknowledgement guidelines available here, please include the following acknowledgment in any published manuscripts or papers: This research was supported in part by the National Science Foundation under Grant No. NSF DMS-10-578.

*All workshop talks and discussion periods will be held in the Simons Center Lecture Hall (Room 102)
*More information of the Food Physics Event on Wednesday November 20th can be seen here.
*The Math Colloquium talk will be held in the Simons Center Lecture Hall (Room 102) on Thursday at 4pm.