What is he best known for?
The fields of study he is best known for:
- Mathematical analysis
- Quantum mechanics
- Algebra
Mathematical analysis, Applied mathematics, Rough path, Markov chain and Ergodicity are his primary areas of study.
His Mathematical analysis research is multidisciplinary, incorporating elements of Invariant measure and Pure mathematics.
His work carried out in the field of Applied mathematics brings together such families of science as Markov process, Group, Measure, Spectral gap and Nonlinear system.
His Rough path study integrates concerns from other disciplines, such as Factorization and Type.
As part of the same scientific family, he usually focuses on Markov chain, concentrating on Lyapunov function and intersecting with Small set, Weak convergence and Open problem.
His Ergodicity research incorporates elements of Ergodic theory, Fractional Brownian motion, Jump and Hurst exponent.
His most cited work include:
- A theory of regularity structures (606 citations)
- Solving the KPZ equation (485 citations)
- Ergodicity of the 2D Navier-Stokes equations with degenerate stochastic forcing (425 citations)
What are the main themes of his work throughout his whole career to date?
Martin Hairer mostly deals with Mathematical analysis, Applied mathematics, Invariant measure, Pure mathematics and White noise.
The study incorporates disciplines such as Fractional Brownian motion, Brownian motion and Ergodicity in addition to Mathematical analysis.
His research in Applied mathematics intersects with topics in Rough path, Measure, Nonlinear system, Gaussian and Random walk.
He has included themes like Exponential function and Bifurcation in his Invariant measure study.
His studies deal with areas such as Space, Initial value problem, Markov chain and Projection as well as Pure mathematics.
His research in White noise intersects with topics in Partial differential equation and Mixing.
He most often published in these fields:
- Mathematical analysis (45.81%)
- Applied mathematics (25.99%)
- Invariant measure (14.98%)
What were the highlights of his more recent work (between 2016-2021)?
- Pure mathematics (14.54%)
- Applied mathematics (25.99%)
- Statistical physics (10.13%)
In recent papers he was focusing on the following fields of study:
His primary areas of study are Pure mathematics, Applied mathematics, Statistical physics, Mathematical analysis and Measure.
His study explores the link between Pure mathematics and topics such as Heat equation that cross with problems in Diffeomorphism, Dirichlet form, Riemannian manifold, Multiplicative function and Rough path.
The study incorporates disciplines such as Stochastic differential equation and Stochastic partial differential equation in addition to Rough path.
His Applied mathematics research includes themes of Discretization, Scale, Universality and White noise.
His work deals with themes such as Fractional Brownian motion and Central limit theorem, which intersect with Mathematical analysis.
The Measure study combines topics in areas such as Invariant measure, Sequence, Corollary and Coupling.
Between 2016 and 2021, his most popular works were:
- A Course on Rough Paths: With an Introduction to Regularity Structures (188 citations)
- Algebraic renormalisation of regularity structures (91 citations)
- Multiplicative stochastic heat equations on the whole space (58 citations)
In his most recent research, the most cited papers focused on:
- Mathematical analysis
- Quantum mechanics
- Algebra
The scientist’s investigation covers issues in Space, Pure mathematics, Statistical physics, Mathematical analysis and Renormalization.
His Space research integrates issues from Discrete mathematics, Group, Type, Stochastic partial differential equation and Class.
His Pure mathematics study combines topics in areas such as Ergodicity, Brownian bridge, Stability theorem and Periodic boundary conditions.
His Statistical physics study combines topics from a wide range of disciplines, such as Cumulant, Leverage and Sine.
His work in the fields of Mathematical analysis, such as Initial value problem, intersects with other areas such as Grid.
His research integrates issues of Rough path, Brownian motion, Differential equation, Stochastic differential equation and Mixing in his study of Gaussian.
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