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Anke Pietsch

Lucas Broux (MPI Leipzig): The Phi4 equation and regularity structures of multi-indices

Tuesday, 12.11.2024 14:15 im Raum SRZ 203

Mathematik und Informatik

This talk will be concerned with some aspects of the renormalization of the Φ4 stochastic partial differential equation, in the singular but subcritical (also called super-renormalizable) range. Recently, a novel perspective on the theory of regularity structures, based on multi-indices rather than trees, has been introduced. This will be the viewpoint taken in this talk. I wish to first introduce the notion of "model", which in this context may be motivated by considering the "geometry" of the solution manifold. Because this model is indexed by multi-indices, which form a much sparser index set than trees, it turns out that Hairer's original fixed-point formulation is not applicable in order to construct an actual solution to the equation from this model. In that regard, I would like to describe a more "intrinsic" strategy for well-posedness which does not rely on a fixed-point formulation and which we implement in a space-time periodic setting. (Based on joint works with Felix Otto, Rhys Steele and Markus Tempelmayr)



Angelegt am 11.09.2024 von Anke Pietsch
Geändert am 30.10.2024 von Claudia Lückert
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