Compactifying Moduli Spaces

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Advanced course / School
From May 27, 2013
to May 31, 2013

Objectives

The Advanced School “Compactifying Moduli Spaces” deals with various instances of moduli spaces in Algebraic Geometry, with particular attention to questions related to compactification. It has three goals: to introduce a new generation of students and researchers to these subjects; to collect and survey recent development in the theory; to formulate and disseminate new problems and directions of research.
 
The geometry of moduli spaces has been widely investigated and it is certainly one of the main subjects in Algebraic Geometry. In particular, moduli spaces of curves gave a major boost to the theory due to their many connections with Theoretical Physics and counting invariants. However, to count invariants it is very useful to apply intersection theory techniques that require the space to be proper, and moduli spaces are usually not proper. The problem of compactifying them is not trivial. Geometric Invariant Theory (GIT) may be a way to tackle the problem, but the limit points can be hard to describe geometrically.
 
Nowadays, new notions of stability and new techniques related to the minimal model program have been combined with GIT to provide new points of view to attack the problem and, more generally, to study the birational geometry of compactified moduli spaces. This has brought back many important insights again about counting invariants and mirror symmetry and has also been used to study other moduli problems, like the moduli of coherent sheaves or the moduli spaces of higher dimensional varieties.
 
The lecturers have been chosen among the leading experts of the area. Following the usual policy of the Advanced Schools at CRM, informal notes will be delivered by the speakers to the participants at the beginning of the school.​

List of Speakers

Valery Alexeev, University of Georgia
Paul Hacking, University of Massachusetts Amherst
Radu Laza, Stony Brook University
Manfred Lehn, Universität Mainz
Dragos Oprea, University of California at San Diego

Organizing committee

Gilberto Bini, Università degli Studi di Milano
Martí Lahoz, Université Paris Sud 11
Emanuele Macrì, The Ohio State University
Paolo Stellari, Università degli Studi di Milano

Scientific committee

Enrico Arbarello, Dipartimento di Matematica “G. Castelnuovo”, “Sapienza” Università di Roma
Aaron Bertram, Department of Mathematics, University of Utah
Bert van Geemen, Dipartimento di Matematica “F.Enriques”, Università degli Studi di Milano
Daniel Huybrechts, Mathematisches Institut, Universität Bonn
Joan Carles Naranjo, Departament d’Àlgebra i Geometria, Universidat de Barcelona​

LIST OF PARTICIPANTS

Armin Schikorra, Max Planck Institute für Mathematiks 
Azahara de la Torre Pedraza, Universitat Politècnica de Catalunya 
Daniele Castorina, Università degli Studi di Roma “Tor Vergata”
Diana Stan, Universidad Autónoma de Madrid 
Enrico Valdinoci, Università di Milano and Weierstrass Institute for Applied Analysis and Stochastics, Berlin
Filomena Feo, Università degli Studi di napoli 
Isabel Coelho, 
Joan Solà-Morales Rubió, Universitat Politècnica de Catalunya 
Joaquín Pérez Muñoz, Universidad de Granada 
Jun Yang, Shenzhen University 
Manel Sanchón, Universitat de Barcelona 
Manon Nys, Université Libre de Bruxelles
Miguel Yangari Sosa, Universidad de Chile 
Nicola Soave, Università degli studi di Milano, 
Serena Dipierro, Universidad de Chile 
Xavier Cabré Vilagut, Universitat Politècnica de Catalunya
Xavier Ros-Oton, Universitat Politècnica de Catalunya

INVOICE/PAYMENT INFORMATION

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For inquiries about this event please contact the Scientific Events Coordinator Ms. Núria Hernández at nhernandez@crm.cat​​

 

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