A Theory of Regularity Structures

Wednesday, January 16, 2013 - 11:30am - 12:20pm
Keller 3-180
Martin Hairer (University of Warwick)
The classical way of measuring the regularity of a function is by comparing it
in the neighbourhood of any point with a polynomial of sufficiently high degree.
Would it be possible to replace monomials by functions with less regular behaviour
or even by distributions? It turns out that the answer to this question has
surprisingly far-reaching consequences for building solution theories for semilinear
PDEs with very rough input signals, revisiting the age-old problem of multiplying
distributions of negative order, and understanding renormalisation theory.
As an application, we build the natural Langevin equation associated
with Phi^4 Euclidean quantum field theory in dimension 3.
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