Multi-valued Harmonicity
Date: 21 - 25 September 2026
Location: Mathematical Institute, University of Oxford
Event type: CRC Workshop
Organisers: Aleksander Doan (UCL), Rafe Mazzeo (Stanford), Clifford Taubes (Harvard)
Harmonic functions which are not single-valued arise in classical complex function theory, but these objects have emerged in several different places in more recent research. Already 50 years ago, Almgren studied the calculus of multi-valued functions in general dimensions as a means to parametrize area-minimizing submanifolds of codimension greater than one, and modern regularity theory in that subject employs this framework as a basic tool.
More recently, multi-valued harmonic 1-forms and spinors have appeared as limiting blowup profiles for certain new gauge theories with nonimpact gauge group, and in addition when characterising degenerations of calibrated submanifolds in Riemannian manifolds with special holonomy.
More recently still, multi-valued harmonicity arises in the context of thin obstacle problems. The new (and perhaps central) features of these objects are their codimension two branching sets, which are the root of many analytic subtleties. There are now many researchers encountering these objects and proving interesting theorems about multi-valued harmonic objects.
This workshop aims to collect experts from these various branches of geometric analysis to illuminate problems and methods that should be useful to the whole community, and to suggest new directions in the field.
Registration: Participation in the workshop is by invitation, but a limited number of additional places is available. To register for the Clay Research Conference or to register interest in a workshop, please email Naomi Kraker, providing the name of your institution and stating which workshop you wish to attend. Students please also provide a letter of reference from your supervisor.
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