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Metric and Analytic Aspects of Moduli Spaces

20th July 2015 to 14th August 2015

Organisers: Sergey Cherkis (Arizona), Nigel Hitchin (Oxford), Rafe Mazzeo (Stanford) and Michael Singer (UCL)

Programme Theme

The term ‘moduli space’ has its origins in the classification of conformal structures on two-dimensional surfaces. Closed surfaces are classified topologically by their genus, but for fixed genus, the set of inequivalent conformal structures is essentially a smooth finite- dimensional manifold, a first example of a moduli space.

In more recent times, many other instances of mathematical structures of this type have come to light, above all in gauge theory. They have had, and continue to have, a major impact in modern geometry, topology and mathematical physics.

Working with moduli spaces is subtle. First of all, they are implicitly defined (typically) as equivalence classes of solutions to some nonlinear partial differential equations. Second, they are almost invariably non-compact and/or singular, and one of the challenges is to understand them asymptotically and/or near the singularities.

The goal of the programme is to explore moduli spaces from the metric and analytical points of view. We shall survey the current state of the art with a focus on four themes: 4-dimensional hyperKaehler manifolds; compactification of moduli spaces; analysis on moduli spaces; new constructions and challenges. There will be a 5-day workshop during the second week of the programme.

University of Cambridge Research Councils UK
    Clay Mathematics Institute The Leverhulme Trust London Mathematical Society Microsoft Research NM Rothschild and Sons