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CRM > English > Activities > Advanced Course "Compactifying Moduli Spaces"
Advanced Course "Compactifying Moduli Spaces"
Dates: May 27 to 31, 2013

Dinner on Wednesday (registration is necessary before Tuesday afternoon) new!

Notes of the course New version! 


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​
To register to the conference, please send an e-mail to no later than April 30, 2013. The participation to the conference is subject to the payment of a registration fee to be made at any time after the registration but before May 19, 2013:
To receive full consideration for support and housing please register by March 20​​

Senior Registration fee: 300 euros

Junior Registration fee (Phd students and post-docs having read the Thesis in the last three years): 150 euros

Local registration fee (researchers affiliated to local universities and members of the Societat Catalana de Matemàtiques): 60 euros
The registration fee (not for locals) covers: attendance to the lectures, documentation package, lunch tickets, coffee breaks, and excursion.

The local registration fee covers: attendance to the lectures, documentation package, and coffee breaks.

In order to pay, please click the registration button at the top of this page and follow the instructions.

Financial Support for Lodging

There will be some financial support to cover lodging expenses of some participants (in double rooms). People interested in this should send and e-mail to the organizers ( mentioning the following information:

- Current position and affiliation.

- Title of the Ph.D. thesis and name of the advisor.

- For Ph.D students: in which year of your Ph.D program are you?

- For Post-docs: when did you get the Ph.D? Give a list of the previous Post-doc positions.

- Name of a potential room-mate.



Participants not receiving financial support should make the reservation for lodging by themselves. We encourage them to do it as soon as possible. Those supported by the Organization should wait for instructions from the Organizers.
In case you want to make a reservation at Vila please send a message to Ms. Marta Roig ( Please be sure to mention the reference "CRM Activity" when making your reservation​.


Vila Universitària 2

In case you want to make a reservation at Vila please send a message to Ms. Marta Roig ( Please be sure to mention the reference "CRM Activity" when making your reservation.

The following services are included:

Weekly Cleaning service.

  • Water and electricity expenses included in the price.
  • Wire internet connection.
  • Bed and towels equipment.
  • Adapted television to the TDT.
  • Free entrance to SAF (sport facilities)

You can visit the Vila web page at the address: www.vilauniversitaria.comThe address is Vila Universitària, Campus Universitat Autònoma de Barcelona. 08193 Bellaterra. You can check how to get there using the local map of the CRMwebpage: Vila Universitària 2 is right on the campus and the closest train station is Bellaterra train station at the FCG train line.

Hotel Campus

In case you want to make a reservation at Hotel Campus please send a message to Please be sure to mention the reference "CRM Activity" when making your reservation.​

Campus Hotel ( 

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"Any opinions, findings, and conclusions or recommendations expressed in this material are those of the organizers, and do not necessarily reflect the views of the National Science Foundation."

Contact information
​​​​If you have any questions please contact:

Ms. Núria Hernandez
Activities Coordinator​