# A theory of regularity structures

@article{Hairer2014ATO,
title={A theory of regularity structures},
author={Martin Hairer},
journal={Inventiones mathematicae},
year={2014},
volume={198},
pages={269-504}
}
• Martin Hairer
• Published 20 March 2013
• Mathematics
• Inventiones mathematicae
We introduce a new notion of “regularity structure” that provides an algebraic framework allowing to describe functions and/or distributions via a kind of “jet” or local Taylor expansion around each point. The main novel idea is to replace the classical polynomial model which is suitable for describing smooth functions by arbitrary models that are purpose-built for the problem at hand. In particular, this allows to describe the local behaviour not only of functions but also of large classes of…
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In order to provide a local description of a regular function in a small neighbourhood of a point x, it is sufficient by Taylor’s theorem to know the value of the function as well as all of its

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