Lorentz Center - Heights and Moduli Spaces from 10 Jun 2013 through 14 Jun 2013
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    Heights and Moduli Spaces
    from 10 Jun 2013 through 14 Jun 2013



The aim of the workshop was to discuss the state of the art in the study of the arithmetic of moduli spaces, and in particular heights on moduli spaces. Moduli spaces belong to the most basic and intensively studied objects in mathematics. They are geometric objects parametrizing other geometric objects of a specific kind, such as curves, abelian varieties or vector bundles. 

Traditionally moduli spaces were studied using topological or analytical methods. This has led to fruitful connections with complex geometry and mathematical physics. Since the breakthrough results of G. Faltings around the so-called Mordell conjecture, in the 80s, arithmetic methods have in addition aroused a lot of interest, and nowadays are in the center of research.

The lectures (21 in total) were loosely centered around four themes: special cycles on Shimura varieties; degeneration of metrics on non-compact moduli varieties; explicit formulas and bounds for heights; and models over p-adic rings. Eight of the lectures were given by PhD students and young postdocs. In the audience, the ratio between junior and senior researchers was about 50 % - 50 %. One of the successful aspects of the conference was this lively mix between key leaders in the field, on the one hand, and promising young new researchers, on the other.

Another remarkable aspect was the joint venture we made for this occasion with the Intercity Number Theory Seminar and the Dutch-Belgian Algebraic Geometry Days: the last Friday of the conference was organized joined with them, and brought an additional number of participants to the Lorentz Center.

A final successful aspect is that many new research contacts have arisen. Many discussions started in front of the whiteboard of the common room, where recent insights were shared, and new research collaborations were initiated. On the whole, there were many interactions, and the participants profited a lot from the open atmosphere created by the open doors and offices at the Lorentz Center. It is sure that many will return, either as a participant of a next conference, or as an organizer.

The Lorentz Center has been an ideal place for our event, with all participants praising the efficient organisation and helpful staff. 

Gerard Freixas i Montplet (U Paris VI)
Gerard van der Geer (U Amsterdam)
Robin de Jong (U Leiden)