# 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.

##### Education & Training
• Ph.D., Princeton University 1998

• M.A., Princeton University 1996

• B.S., Yale University 1992

Mattingly, J. C. “Contractivity and ergodicity of the random map x →.” Theory of Probability and Its Applications, vol. 47, no. 2, June 2003, pp. 333–43. Scopus, doi:10.1137/S0040585X97979767. Full Text Open Access Copy

Mattingly, Jonathan C. On recent progress for the stochastic Navier Stokes equations. Univ. Nantes, Nantes, 2003, p. Exp.No.XI-52.

Mattingly, J. C. “The dissipative scale of the stochastics Navier-Stokes equation: Regularization and analyticity.” Journal of Statistical Physics, vol. 108, no. 5–6, Dec. 2002, pp. 1157–79. Scopus, doi:10.1023/A:1019799700126. Full Text

Mattingly, J. C. “Exponential convergence for the stochastically forced Navier-Stokes equations and other partially dissipative dynamics.” Communications in Mathematical Physics, vol. 230, no. 3, Nov. 2002, pp. 421–62. Scopus, doi:10.1007/s00220-002-0688-1. Full Text

Mattingly, J. C., et al. “Ergodicity for SDEs and approximations: Locally Lipschitz vector fields and degenerate noise.” Stochastic Processes and Their Applications, vol. 101, no. 2, Oct. 2002, pp. 185–232. Scopus, doi:10.1016/S0304-4149(02)00150-3. Full Text

Mattingly, J. C., and A. M. Stuart. “Geometric ergodicity of some hypo-elliptic diffusions for particle motions.” Markov Processes and Related Fields, vol. 8, 2002, pp. 199–214.

Mattingly, Jonathan Christopher. “Contractivity and ergodicity of the random map $x\mapsto|x-\theta|$.” Teoriya Veroyatnostei I Ee Primeneniya, vol. 47, no. 2, Steklov Mathematical Institute, 2002, pp. 388–97. Crossref, doi:10.4213/tvp3671. Full Text Open Access Copy

Weinan, E., et al. “Gibbsian dynamics and ergodicity for the stochastically forced Navier-Stokes equation.” Communications in Mathematical Physics, vol. 224, no. 1, Dec. 2001, pp. 83–106. Scopus, doi:10.1007/s002201224083. Full Text

Weinan, E., and J. C. Mattingly. “Ergodicity for the navier-stokes equation with degenerate random forcing: Finite-dimensional approximation.” Communications on Pure and Applied Mathematics, vol. 54, no. 11, Nov. 2001, pp. 1386–402. Scopus, doi:10.1002/cpa.10007. Full Text Open Access Copy