# Jonathan Christopher Mattingly

- James B. Duke Distinguished Professor
- Professor of Mathematics
- Chair of the Department of Mathematics

### Research Areas and Keywords

##### Analysis

Stochastic Analysis, Malliavin Calculus, Ergodic Theory

##### Biological Modeling

Stochastic and Random PDEs, Stochastic Dynamical Systems, Mathematical Ecology and Evolution, Metabolic and Cellular modeling, Out of equilibrium statistical mechanics

##### Computational Mathematics

Markov Chain Mixing, Stochastic Numerical Methods, High Dimensional Random Algorithms

##### PDE & Dynamical Systems

Stochastic and Random PDEs, Stochastic Dynamical Systems, Malliavin Calculus, Fluid Mechanics, Approximating invariant measures

##### Physical Modeling

Stochastic and Random PDEs, Stochastic Dynamical Systems, Fluid Mechanics

##### Probability

Stochastic and Random PDEs, Stochastic Dynamical Systems, Stochastic Analysis, Malliavin Calculus, Markov Chain Mixing, Ergodic Theory, High Dimensional Random Algorithms, Probability on stratified spaces, Out of equilibrium statistical mechanics, Approximating invariant measures

Jonathan Christopher Mattingly grew up in Charlotte, NC where he attended Irwin Ave elementary and Charlotte Country Day. He graduated from the NC School of Science and Mathematics and received a BS is Applied Mathematics with a concentration in physics from Yale University. After two years abroad with a year spent at ENS Lyon studying nonlinear and statistical physics on a Rotary Fellowship, he returned to the US to attend Princeton University where he obtained a PhD in Applied and Computational Mathematics in 1998. After 4 years as a Szego assistant professor at Stanford University and a year as a member of the IAS in Princeton, he moved to Duke in 2003. He is currently a Professor of Mathematics and of Statistical Science.

His expertise is in the longtime behavior of stochastic system including randomly forced fluid dynamics, turbulence, stochastic algorithms used in molecular dynamics and Bayesian sampling, and stochasticity in biochemical networks.

He is the recipient of a Sloan Fellowship and a PECASE CAREER award. He is also a fellow of the IMS and the AMS.

Hairer, M., and J. C. Mattingly. “A theory of hypoellipticity and unique ergodicity for semilinear stochastic PDEs.” *Electronic Journal of Probability*, vol. 16, 2011, pp. 658–738.
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Koelle, K., et al. “A dimensionless number for understanding the evolutionary dynamics of antigenically variable RNA viruses.” *Proceedings of the Royal Society B: Biological Sciences*, vol. 278, no. 1725, 2011, pp. 3723–30. *Scival*, doi:10.1098/rspb.2011.0435.
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Mattingly, J. C., et al. “Convergence of numerical time-averaging and stationary measures via Poisson equations.” *Siam Journal on Numerical Analysis*, vol. 48, no. 2, 2010, pp. 552–77. *Scival*, doi:10.1137/090770527.
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Hairer, M., and J. C. Mattingly. “Slow energy dissipation in anharmonic oscillator chains.” *Communications on Pure and Applied Mathematics*, vol. 62, no. 8, 2009, pp. 999–1032. *Scival*, doi:10.1002/cpa.20280.
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Iyer, G., and J. Mattingly. “A stochastic-Lagrangian particle system for the Navier-Stokes equations.” *Nonlinearity*, vol. 21, no. 11, Nov. 2008, pp. 2537–53. *Scopus*, doi:10.1088/0951-7715/21/11/004.
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Martin Hairer, Jonathan C. “Spectral gaps in Wasserstein distances and the 2D stochastic Navier-Stokes equations.” *Annals of Probability*, no. 6, 2008, pp. 993–1032.

Mattingly, J. C., et al. “Simple systems with anomalous dissipation and energy cascade.” *Communications in Mathematical Physics*, vol. 276, no. 1, Nov. 2007, pp. 189–220. *Scopus*, doi:10.1007/s00220-007-0333-0.
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Bakhtin, Y., and J. C. Mattingly. “Malliavin calculus for infinite-dimensional systems with additive noise.” *Journal of Functional Analysis*, vol. 249, no. 2, Aug. 2007, pp. 307–53. *Scopus*, doi:10.1016/j.jfa.2007.02.011.
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Anderson, David F., et al. “Propagation of fluctuations in biochemical systems, I: linear SSC networks.” *Bulletin of Mathematical Biology*, vol. 69, no. 6, Aug. 2007, pp. 1791–813. *Epmc*, doi:10.1007/s11538-007-9192-2.
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Lamba, H., et al. “An adaptive Euler-Maruyama scheme for SDEs: Convergence and stability.” *Ima Journal of Numerical Analysis*, vol. 27, no. 3, July 2007, pp. 479–506. *Scopus*, doi:10.1093/imanum/drl032.
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