= Martin Hairer
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<Martin Hairer> is a <mathematician> whose work joins <probability theory> and <analysis>. He developed <regularity structures> to give precise meaning to classes of singular <stochastic partial differential equations>. His EPFL biography identifies this work as central to his 2014 Fields Medal.https://www.epfl.ch/labs/propde/prof-martin-hairer/[Institutional biography and principal publications]{ref}
The motivating obstacle is that a noisy solution can be too irregular for the nonlinear operations appearing in its own equation. Smoothing the input makes an ordinary equation possible, but the resulting solutions need not converge when the smoothing is removed. <Regularity structures> replace ordinary polynomial local expansions with expansions tailored to the singular input and organize the necessary corrections. The theory proves convergence of appropriate corrected approximations for the equations it covers.<A theory of regularity structures by Martin Hairer>[Abstract and Introduction: local expansions, nonlinear operations and renormalized approximation]{ref}
His <An Introduction to Stochastic PDEs by Martin Hairer> gives a complementary starting point through the <stochastic heat equation> and <mild solutions>. Integrating the heat evolution against a random driving term clarifies why solving a noisy equation requires specifying both the evolution operator and the interpretation of the noise.<An Introduction to Stochastic PDEs by Martin Hairer>[Sections 2 and 5: motivating equations and stochastic convolution]{ref}
\Image[https://people.epfl.ch/private/common/photos/links/357109.jpg?ts=1668698389]
{title=<Martin Hairer>, portrait linked from his EPFL research-group biography}
{description=External institutional portrait.}
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