The summer school entitled "Compactifying Moduli Spaces" will take place at the Centre de Recerca Matematica (CRM) in Barcelona, Spain from May 27 to 31, 2013. The theme of the school is the different aspects of moduli spaces in algebraic geometry, with particular attention to questions related to compactification. Compactness is a fundamental property needed in order to apply degeneration techniques (e.g., for Brill-Noether type arguments) and for intersection theory (e.g., to define Gromov-Witten invariants). Generally, a natural moduli problem is not compact: understanding how to compactify the moduli space and how this compactification depends on choices is the main topic of the school. We will focus on two moduli problems: the moduli of varieties and the moduli of vector bundles.
The school has three goals: to introduce a new generation of students and researchers to the subject; to collect and survey recent development in the theory of moduli spaces; to formulate and disseminate new problems and directions of research. There will be five mini-courses, given by the leading experts in the field. The lectures will be complemented by afternoon sessions, where young algebraic geometers will present their work and explain examples and further insights on the material seen in the main courses. This funding will be used to support the participation in the summer school of graduate students and young postdocs from universities in the U.S. The conference website is www.crm.cat/en/Activities/Pages/ActivityDescriptions/Compactifying-Moduli-Spaces.aspx
The main goal of the project was to fund about 10 PhD students and young postdocs, coming from US universities, to attend the summer school ``Compactifying Moduli Spaces'', held at CRM, Barcelona, Spain, May 27-31, 2013. The website for the school is: www.crm.cat/en/Activities/Pages/ActivityDescriptions/Compactifying-Moduli-Spaces.aspx The area of research for the school is Algebraic Geometry. More precisely, the main idea was both to survey recent progresses in questions related to moduli spaces, either of varieties or vector bundles, and also to present foundational material to understand them. There were 5 minicourses, presented by leading experts in the field: Valery Alexeev (University of Georgia) ``Moduli of weighted stable hyperplane arrangements, with applications'' Paul Hacking (University of Massachusetts Amherst) ``Compact moduli spaces of surfaces and exceptional vector bundles'' Radu Laza (Stony Brook University) ``Perspectives on the compactification problem for moduli spaces'' Manfred Lehn (Universität Mainz) ``Moduli of rational curves'' Dragos Oprea (University of California at San Diego) ``The moduli space of stable quotients'' We were able to fund 11 PhD students and 1 postdoc, coming from US universities. We also used other sources of funding to cover (part of) the expenses for the other participants. The total number of PhD students and young researcher attending the school was about 70, while the total number of participants was about 80. The lecture notes for the 5 mini-courses are available on-line at the school website. The plan is to revise these notes and write a two volumes book, to be published in the CRM special series with Birkauser. Currently, three sets of lecture notes are already revised and in the refereeing process.
