14 novembre 2017

Svitlana Mayboroda (Université du Minnesota)
Harmonic measure for lower dimensional sets

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Lieu : Salle 113-115 (Bâtiment 425)

Résumé : Harmonic measure and harmonic functions more generally play a unique role in geometric measure theory : boundedness of the harmonic Riesz transform is equivalent to uniform rectifiability of sets, so is the boundedness of the harmonic square function, to mention only a few results. Unfortunately, the concept of a harmonic measure is intrinsically restricted to co-dimension 1. In this talk, we introduce a new notion of a « harmonic » measure, associated to a suitable degenerate PDE, which serves the higher co-dimensions. We discuss its basic properties and interplay between absolute continuity of our harmonic measure with respect to the Hausdorff measure, square function estimates, and rectifiability of a lower-dimensional set.
This is joint work with Guy David, Max Engelstein, Joseph Feneuil, and Zihui Zhao.

Harmonic measure for lower dimensional sets  Version PDF

Dmitri Wyss (IMJ)
p-adic integration along the Hitchin fibration

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Lieu : Bât. 425, salle 117-119

Résumé : In my talk I will explain how to use p-adic integration and the global geometry of the moduli space of Higgs bundles to count points on (possibly singular) Hitchin fibers. An application of this idea is the proof of the topological mirror symmetry conjecture by Hausel-Thaddeus, which predicts an equality of Hodge numbers of certain SLn and PGLn-Higgs moduli spaces. This is joint work Michael Groechening and Paul Ziegler.

p-adic integration along the Hitchin fibration  Version PDF