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Metric and Analytic Aspects of Moduli Spaces

Participation in INI programmes is by invitation only. Anyone wishing to apply to participate in the associated workshop(s) should use the relevant workshop application form.

20th July 2015 to 14th August 2015
Sergey Cherkis University of Arizona
Nigel Hitchin University of Oxford
Rafe Mazzeo Stanford University
Michael Singer University College London


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 London Mathematical Society NM Rothschild and Sons