X Lisbon Summer Lectures in Geometry

Lectures by

• Kai Behrend (University of British Columbia, Canada), 
  Moduli Spaces via differential graded Lie algebras

Abstract: I will explain how many interesting moduli spaces in algebraic geometry can be constructed as the solution set of the Maurer-Cartan equation in a differential graded Lie algebra, modulo the action of the gauge group. The advantage of this approach is that it gives directly the higher derived structure on the moduli space in question. We will focus on the case of sheaves on projective varieties. We will examine the case of the Hilbert scheme of points on a Calabi-Yau threefold in particular detail.

Referências:
Deformation theory via differential graded Lie algebras - Marco Manetti
Lectures on deformations of complex manifolds - Marco Manetti
Injective resolutions of BG and derived moduli spaces of local systems - M. Kapranov
A functorial construction of moduli of sheaves - Luis Álvarez-Cónsul, Alastair King


• Dietmar Salamon (ETH Zurich, Switzerland), 
  Floer homology

1. Floer homology groups in symplectic topology I
2. Floer homology groups in symplectic topology II
3. The Atiyah-Floer conjecture and 3-manifolds with boundary
4. Floer homology groups in hyperkaehler geometry

Tentative schedule

• Center for Mathematical Analysis, Geometry and Dynamical Systems - IST (Lisbon)
• Fundação para a Ciência e a Tecnologia

• XVIIIth Oporto Meeting on Geometry, Topology and Physics, 9-12/July/2009,
  with minicourses by Paul Biran, Henrique Bursztyn, Yael Karshon and Alan Weinstein.


• Geometry Summer School, 13-17/July/2009,
  with minicourses by Miguel Abreu, János Kollár, Alina Marian, Rahul Pandharipande and Alan Weinstein.


• The IST String Fest, 29/June to 1/July/2009.


• Mathematical Relativity in Lisbon, 18-19/June/2009.