Martin Hairer | Academic Influence

Why Is Martin Hairer Influential?

Sir Martin Hairer is currently a professor of mathematics and Chair in Probability and Stochastic Analysis at Imperial College London in the Faculty of Natural Sciences, Department of Mathematics. Previously, he held roles at the University of Warwick, and the Courant Institute of New York University. An Austrian Citizen born in Geneva, Switzerland, Hairer completed his BS in mathematics at the University of Geneva in 1994. He stayed there for his MS and PhD in physics, completed in 2001.

Hairer is known as the leading name in stochastic partial differential equations, with significant implications for areas including quantum field theory and spatial modeling. In his research, Hairer has produced groundbreaking results in the construction of stochastic systems, stochastic analysis techniques, and his theory of regularity structures, fueling further research and advancement.

For his work, Hairer has received awards and honors including the 2014 Fields Medal, the Whitehead Prize, an Advanced Research Fellowship with the Engineering and Physical Sciences Research Council, Fellowship with the Royal Society, and holds the honorary title of Knight Commander of the Order of the British Empire.

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According to Wikipedia, Sir Martin Hairer is an Austrian-British mathematician working in the field of stochastic analysis, in particular stochastic partial differential equations. He is Professor of Mathematics at Imperial College London, having previously held appointments at the University of Warwick and the Courant Institute of New York University. In 2014 he was awarded the Fields Medal, one of the highest honours a mathematician can achieve. In 2020 he won the 2021 Breakthrough Prize in Mathematics.

Martin Hairer's Published Works

A theory of regularity structures
Solving the KPZ equation
Ergodicity of the 2D Navier-Stokes equations with degenerate stochastic forcing
A Course on Rough Paths
Yet Another Look at Harris’ Ergodic Theorem for Markov Chains
A Course on Rough Paths: With an Introduction to Regularity Structures
An Introduction to Stochastic PDEs
Asymptotic coupling and a general form of Harris’ theorem with applications to stochastic delay equations
Spectral gaps in Wasserstein distances and the 2D stochastic Navier–Stokes equations
Non-Equilibrium Statistical Mechanics¶of Strongly Anharmonic Chains of Oscillators
Algebraic renormalisation of regularity structures
Exponential mixing properties of stochastic PDEs through asymptotic coupling
A Wong-Zakai theorem for stochastic PDEs
Spectral gaps for a Metropolis–Hastings algorithm in infinite dimensions
Sampling the posterior: An approach to non-Gaussian data assimilation
ANALYSIS OF SPDES ARISING IN PATH SAMPLING PART II: THE NONLINEAR CASE
A CLASS OF GROWTH MODELS RESCALING TO KPZ
An analytic BPHZ theorem for regularity structures
Exponential ergodicity for Markov processes with random switching
A Theory of Hypoellipticity and Unique Ergodicity for Semilinear Stochastic PDEs
Spectral Properties of Hypoelliptic Operators
Uniqueness of the Invariant Measure¶for a Stochastic PDE Driven by Degenerate Noise
A simple framework to justify linear response theory
Ergodicity of stochastic differential equations driven by fractional Brownian motion
Multiplicative stochastic heat equations on the whole space
Introduction to Regularity Structures
A version of Hörmander’s theorem for the fractional Brownian motion
Analysis of SPDEs arising in path sampling. Part I: The Gaussian case
Loss of regularity for Kolmogorov equations
Rough Stochastic PDEs
On Malliavinʼs proof of Hörmanderʼs theorem
Non-asymptotic mixing of the MALA algorithm
A central limit theorem for the KPZ equation
Smoothness of the density for solutions to Gaussian rough differential equations
Regularity of laws and ergodicity of hypoelliptic SDEs driven by rough paths
Renormalising SPDEs in regularity structures
Geometric versus non-geometric rough paths
Discretisations of rough stochastic PDEs
Ergodicity of hypoelliptic SDEs driven by fractional Brownian motion
Large deviations for white-noise driven, nonlinear stochastic PDEs in two and three dimensions
Slow energy dissipation in anharmonic oscillator chains
The Dynamical Sine-Gordon Model
Periodic Homogenization for Hypoelliptic Diffusions
Triviality of the 2D stochastic Allen-Cahn equation
From Ballistic to Diffusive Behavior in Periodic Potentials
Convergence of Markov Processes August
Rough Burgers-like equations with multiplicative noise
Ergodic theory for SDEs with extrinsic memory
A simple construction of the continuum parabolic Anderson model on $\mathbf{R}^2$
The strong Feller property for singular stochastic PDEs
Approximations to the Stochastic Burgers Equation
The motion of a random string
Signal processing problems on function space: Bayesian formulation, stochastic PDEs and effective MCMC methods
Approximating rough stochastic PDEs
Invariant Measures for Stochastic PDE's in Unbounded Domains
Multiscale analysis for stochastic partial differential equations with quadratic nonlinearities
Random homogenisation of a highly oscillatory singular potential
How Hot Can a Heat Bath Get?
Multiscale Expansion of Invariant Measures for SPDEs
The reconstruction theorem in Besov spaces
Homogenization of periodic linear degenerate PDEs
Averaging dynamics driven by fractional Brownian motion.
GniCodes - Matlab programs for geometric numerical integration
Singular stochastic PDEs
A solution theory for quasilinear singular SPDEs
Singular SPDEs in domains with boundaries
Sampling conditioned diffusions
Rigorous Remarks about Scaling Laws in Turbulent Fluids
Ergodic Properties of Markov Processes
Geometric stochastic heat equations
Ergodic properties of a class of non-Markovian processes
Ergodic properties of highly degenerate 2D stochastic Navier–Stokes equations
Ornstein-Uhlenbeck processes on Lie groups
Regularity structures and the dynamical Φ 43 model
Non-equilibrium steady states for networks of oscillators
Discretisation of regularity structures
An analyst's take on the BPHZ theorem
Ergodic theory for Stochastic PDEs
A spatial version of the Itô–Stratonovich correction
Sampling conditioned hypoelliptic diffusions
Malliavin calculus for highly degenerate 2D stochastic Navier–Stokes equations
A fractional kinetic process describing the intermediate time behaviour of cellular flows
Stationary distributions for diffusions with inert drift
Large-scale limit of interface fluctuation models
A version of H¨ ormander's theorem for the fractional
Improved diffusion Monte Carlo
H\"ormander's theorem for semilinear SPDEs.
Large scale behaviour of 3D continuous phase coexistence models
Singular perturbations to semilinear stochastic heat equations
A Bayesian Approach to Data Assimilation
Regularity structures and the dynamical $\Phi^4_3$ model
Stationary Solutions for a Model of Amorphous Thin-Film Growth
Amplitude Equations for Spdes: Approximate Centre Manifolds and Invariant Measures
Large scale behaviour of 3D phase coexistence models
Exponential mixing for a stochastic partial differential equation driven by degenerate noise
Weak error estimates for trajectories of SPDEs for Spectral Galerkin discretization
Periodic homogenization with an interface: The multi-dimensional case
Optimal rate of convergence for stochastic Burgers-type equations
From averaging to homogenization in cellular flows - an exact description of the transition
A probabilistic argument for the controllability of conservative systems
Large‐Scale Behavior of Three‐Dimensional Continuous Phase Coexistence Models
STOCHASTIC SWIFT-HOHENBERG EQUATION NEAR A CHANGE OF STABILITY
The support of singular stochastic PDEs
Langevin dynamic for the 2D Yang-Mills measure
COUPLING STOCHASTIC PDES
Renormalisation of parabolic stochastic PDEs
Fluctuations Around a Homogenised Semilinear Random PDE
Periodic homogenization with an interface: The one-dimensional case
A chain of interacting particles under strain
Tightness of the Ising–Kac Model on the Two-Dimensional Torus
Renormalisation of Stochastic Partial Differential Equations
Hypoellipticity in Infinite Dimensions
Stochastic Partial Differential Equations on Evolving Surfaces and Evolving Riemannian Manifolds
Malliavin calculus and ergodic properties of highly degenerate 2D stochastic Navier--Stokes equation
Convergence of Markov Processes January 13 , 2016
Some Remarks on Stabilization by Additive Noise
The Brownian Fan
Remarks on the K41 scaling law in turbulent fluids
Exponential Mixing Properties of Stochastic PDEs
Periodic homogenization with an interface
Improved diffusion Monte Carlo and the Brownian fan
A Noise-Induced Transition in the Lorenz System
N ov 2 01 7 Singular SPDEs in domains with boundaries November 10 , 2017
ERGODIC THEORY FOR SDEs WITH EXTRINSIC MEMORY1
Erratum to: Rough Burgers-like equations with multiplicative noise
Slow energy dissipation in chains of anharmonic oscillators December 11 , 2007
An Introduction to Stochastic PDEs January 26 , 2009
Introduction to Hypoelliptic Schrödinger type operators
Advanced stochastic analysis
ON MARTIN HAIRER’S THEORY OF REGULARITY STRUCTURES
0 40 30 03 v 1 3 M ar 2 00 4 Periodic Homogenization for Hypoelliptic Diffusions
Stochastic integration and Ito's formula
On the controllability of conservative systems
Modulation Equations : Stochastic Bifurcation in Large Domains November 23 , 2004
The motion of a random string August 10 , 2016
Application to the KPZ Equation
A fresh look on the Phi^4 model
A ug 2 00 9 Sampling Conditioned Hypoelliptic Diffusions
A scaling limit of the parabolic Anderson model with exclusion interaction
Stochastic Analysis: Geometry of Random Processes
Let B be standard d-dimensional Brownian motion and v a bounded measurable vector field on ∂
Ergodicity of hypoeliptic SDEs driven by fractional Brownian motion
ar 2 00 4 Ergodicity of Stochastic Differential Equations Driven by Fractional Brownian Motion February 1 , 2008
Multiscale expansion of invariant measures for SPDEs September 30 , 2003
A P ] 4 F eb 2 01 8 Renormalising SPDEs in regularity structures
PR ] 1 2 A pr 2 00 8 Stationary distributions for diffusions with inert drift ∗
Large-scale limit of interface fluctuation models February 23 , 2018
Communications in Mathematical Physics Modulation Equations : Stochastic Bifurcation in Large Domains
Stochastic Modulation Equations
October 2014 Cover English
The reconstruction theorem in Besov spaces September 16 , 2016
Stochastic Partial Differential Equations
A central limit theorem for the KPZ equation July 5 , 2015
A pr 2 00 3 Ergodicity of Stochastic Differential Equations Driven by Fractional Brownian Motion February 20 , 2008
The dynamical sine-Gordon model September 18 , 2014
N ov 2 00 6 Multiscale Analysis for SPDEs with Quadratic Nonlinearities May 14
Operations on controlled rough paths
Periodic Homogenization for Hypoelliptic Diffusions March
PR ] 8 A ug 2 01 8 The dynamical sine-Gordon model in the full subcritical regime August 9 , 2018
15 S ep 2 00 0 Uniqueness of the Invariant Measure for a Stochastic PDE Driven by Degenerate Noise February 8 , 2008
Doob-Meyer type decomposition for rough paths
Advanced functional analysis
Rédacteurs en chef / Chief Editors
Introduction to Regularity Structures August 29 , 2013
Gaussian rough paths
Ja n 20 06 Analysis of SPDEs Arising in Path Sampling Part II : The Nonlinear Case February 27 , 2008
Averaging dynamics driven by fractional Brownian motion February 28 , 2019
PR ] 2 3 Fe b 20 21 The Φ 43 measure has sub-Gaussian tails February
N ov 2 01 7 Singular SPDEs in domains with boundaries July 23 , 2020
The Brownian Web as a random $\mathbb R$-tree
Brownian motion as a rough path
Large-scale limit of interface fluctuation models August 27 , 2018
The space of rough paths
ormander's theorem for the fractional Brownian motion
Operations on Modelled Distributions
A Fields Medal for
S ep 2 01 4 The dynamical sine-Gordon model
Stochastic Analysis: Around the KPZ Universality Class
E LEMENTS OF P ROBABILITY THEORY 2 2 Elements of Probability theory
Stochastic PDEs with multiscale structure
Solutions to rough differential equations
Convergence of Markov Processes
Integration against rough paths
N ov 2 00 6 Multiscale Analysis for SPDEs with Quadratic Nonlinearities February 2 , 2008
Discretisations of rough stochastic PDEs December
Multiscale Analysis for SPDEs with Quadratic Nonlinearities November 28 , 2006
A P ] 2 9 M ar 2 01 8 Multiplicative stochastic heat equations on the whole space September 30 , 2018
Cameron–Martin Regularity and Applications
0 A ug 2 00 4 Modulation Equations : Stochastic Bifurcation in Large Domains February 7 , 2008
Singular perturbations to semilinear stochastic heat equations April 1 , 2010
Ergodic theory for SDEs with extrinsic memory April
0 50 60 64 v 1 2 4 Ju n 20 05 On the controllability of conservative systems
Preface Since its original development in the mid-nineties by Terry Lyons , culminating in the landmark paper
Stochastic differential equations
0 Ju l 2 00 2 Spectral Properties of Hypoelliptic Operators
Ju l 2 00 5 Remarks on the K 41 scaling law in turbulent fluids
N ov 2 01 7 Singular SPDEs in domains with boundaries September 1 , 2018
Ju l 2 01 7 Discretisations of rough stochastic PDEs September 30 , 2018
0 20 40 44 v 1 2 3 A pr 2 00 2 Stationary solutions for a model of amorphous thin-film growth February 7 , 2008
The reconstruction theorem in Besov spaces August 25 , 2018
The Brownian Castle
Introduction to Regularity Structures March 27 , 2014
Corrigendum: Improved Diffusion Monte Carlo

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