Hilbert schemes, sheaves and representations

2013 meeting of the Vector Bundles on Algebraic Curves Group

Trieste, June 17 - 21, 2013

Supported by SISSA, PRIN "Geometry of Algebraic Varieties", and INDAM-GNSAGA.


Scientific Committee: Peter Newstead (Chair), Usha Bhosle, Steven Bradlow, Leticia Brambila-Paz, Ugo Bruzzo, Carlos Florentino, Oscar Garcia-Prada, Peter Gothen, Daniel Hernandez Ruiperez, Alastair King, Herbert Lange, Antony Maciocia, Ignasi Mundet i Riera, Christian Pauly, Alexander Schmitt, Andras Szenes.

Organizing Committee: U. Bruzzo (SISSA), A. Lo Giudice (SISSA), M. Pedrini (SISSA), F. Sala (Heriot-Watt University at Edinburgh), A. Tanzini (SISSA).



Hilbert schemes of points are a traditional field of interest for algebraic geometers. Work by Nakajima and others established a relation between their geometry and the representation theory of Heisenberg-Clifford algebras. More recent research connected Hilbert schemes with other infinite-dimensional algebras, such as Cherednik algebras, quantum Heisenberg algebras, Kac-Moody algebras, and so on. This conference aims at providing an updated survey of the state of the art in this area of research in its various aspects.

Topics will include

categorification of the (quantized) Heisenberg algebra

Cherednik algebras, W-algebras

Ding-Iohara algebras, shuffle algebras

moduli spaces of instantons and framed sheaves

instanton counting, Alday-Gaiotto-Tachikawa conjecture

instanton counting with surfaces operators, moduli spaces of parabolic framed sheaves on Laumon spaces

moduli spaces of quiver representations, wall-crossing formulas

Confirmed speakers include

S. Cautis (University of Southern California)

D. E. Diaconescu (Rutgers University)

M. Finkelberg (IMU, IITP and State University High School of Economics, Moscow)

I. Gordon (University of Edinburgh)

L. Göttsche (ICTP, Trieste)

M. Kool (Imperial College, London)

M. Jardim (Universidade Estadual de Campinas)

A. Negut (Columbia University)

J. V. Rennemo (Imperial College, London)

L. Rybnikov (IITP and State University High School of Economics, Moscow)

A. Savage (University of Ottawa)

R. J. Szabo (Heriot-Watt University, Edinburgh)

A. Tikhomirov (Yaroslavl State Pedagogical University)