Isaac Newton Institute for Mathematical Sciences

Moduli Spaces

4 January - 1 July 2011

Organisers: Professor PE Newstead (Liverpool), Professor L Brambila-Paz (CIMAT, Mexico),
Professor O García-Prada (CSIC, Madrid) and Professor R Thomas (Imperial College London)

Programme Theme

Algebraic geometry is a key area of mathematical research of international significance. It has strong connections with many other areas of mathematics (differential geometry, topology, number theory, representation theory, etc.) and also with other disciplines (in the present context, particularly theoretical physics). Moduli theory is the study of the way in which objects in algebraic geometry (or in other areas of mathematics) vary in families and is fundamental to an understanding of the objects themselves. The theory goes back at least to Riemann in the mid-nineteenth century, but moduli spaces were first rigorously constructed in the 1960s by Mumford and others. The theory has continued to develop since then, perhaps most notably with the infusion of ideas from physics after 1980.

The programme will focus on the following topics:

We should emphasise that the topics are not independent. There are obvious links between (i) and (ii), while (iv) has already had an impact on all the other topics and we believe that this impact is likely to get stronger.

The central aims of the programme are to bring together experts in various aspects of moduli theory and related areas, to advance these topics, and to introduce research students and post-docs to the welath of ideas and problems in them. As stated above, the interdependence of the topics we have identified is crucial to the development of the theory, and a major goal is to develop these ideas further. The programme will include an instructional course and three further workshops, one of which will be held outside Cambridge.