# 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.

### Selected Grants

HDR TRIPODS: Innovations in Data Science: Integrating Stochastic Modeling, Data Representation, and Algorithms awarded by National Science Foundation (Senior Investigator). 2019 to 2022

Collaborative research: Propagation of dissipation: Stochastic stabilization in finite and infinite dimensions awarded by National Science Foundation (Principal Investigator). 2016 to 2020

Quantifying Gerrymandering in the North Carolina Legislature awarded by (Principal Investigator). 2019

BIGDATA:F: Scalable Bayes uncertainty quantification with guarantees awarded by National Science Foundation (Co-Principal Investigator). 2015 to 2019

Analysis and design of robust rare event simulation methods for protein folding and d awarded by University of Chicago (Principal Investigator). 2013 to 2018

Southeastern Probability Conference 2017: Special Edition Interacting Particle Systems with Applications in Biology, Ecology, and Statistical Physics awarded by National Science Foundation (Principal Investigator). 2017 to 2018

EMSW21-RTG: awarded by National Science Foundation (Co-Principal Investigator). 2010 to 2017

Multiscale Analysis of Dynamic Graphs awarded by Office of Naval Research (Co-Principal Investigator). 2012 to 2016

FRG: Collaborative Proposal: awarded by National Science Foundation (Principal Investigator). 2009 to 2013

CAREER: Stochastic Analysis and Numerics in Partial Differential Equations and Extended Dynamical Systems awarded by National Science Foundation (Principal Investigator). 2005 to 2011

## Pages

Lu, Yulong, and Jonathan C. Mattingly. “Geometric ergodicity of Langevin dynamics with Coulomb interactions.” *Nonlinearity*, vol. 33, no. 2, IOP Publishing, Feb. 2020, pp. 675–99. *Crossref*, doi:10.1088/1361-6544/ab514a.
Full Text Open Access Copy

Herzog, David P., and Jonathan C. Mattingly. “Ergodicity and Lyapunov Functions for Langevin Dynamics with Singular Potentials.” *Communications on Pure and Applied Mathematics*, vol. 72, no. 10, WILEY, Oct. 2019, pp. 2231–55. *Wos*, doi:10.1002/cpa.21862.
Full Text Open Access Copy

Chin, Andrew, et al. “The Signature of Gerrymandering in Rucho v. Common Cause.” *South Carolina Law Review*, vol. 70, 2019.

Herschlag, G., et al. *Evaluating Partisan Gerrymandering in Wisconsin*. Sept. 2017.
Open Access Copy

Bakhtin, Y., et al. *Smooth invariant densities for random switching on the torus*. Aug. 2017.
Open Access Copy

Johndrow, J. E., and J. C. Mattingly. *Coupling and Decoupling to bound an approximating Markov Chain*. July 2017.
Open Access Copy

Glatt-Holtz, N. E., et al. “Scaling and Saturation in Infinite-Dimensional Control Problems with
Applications to Stochastic Partial Differential Equations.” *Annals of Pde*, June 2017.
Open Access Copy

Glatt-Holtz, N., et al. “On Unique Ergodicity in Nonlinear Stochastic Partial Differential Equations.” *Journal of Statistical Physics*, vol. 166, no. 3–4, Feb. 2017, pp. 618–49. *Scopus*, doi:10.1007/s10955-016-1605-x.
Full Text Open Access Copy

Cooke, B., et al. “Geometric ergodicity of two-dimensional hamiltonian systems with a Lennard-Jones-like repulsive potential.” *Communications in Mathematical Sciences*, vol. 15, no. 7, Jan. 2017, pp. 1987–2025. *Scopus*, doi:10.4310/CMS.2017.v15.n7.a10.
Full Text Open Access Copy

Hairer, M., and J. Mattingly. *The strong Feller property for singular stochastic PDEs*. 2016.
Open Access Copy

## Pages

Mattingly, Jonathan C., and Toufic M. Suidan. *Transition measures for the stochastic Burgers equation*. American Mathematical Society, 2008, pp. 409–18. *Crossref*, doi:10.1090/conm/458/08950.
Full Text

Carter, Daniel, et al. *A Merge-Split Proposal for Reversible Monte Carlo Markov Chain Sampling of Redistricting Plans*.

Carter, Daniel, et al. *Optimal Legislative County Clustering in North Carolina*.

Holmes, P. J., et al. *Low-Dimensional Models of Turbulence*. Springer Netherlands, 2001, pp. 177–215. *Crossref*, doi:10.1007/978-94-010-0732-0_7.
Full Text

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The work of James B. Duke Professor of Mathematics Jonathan Mattingly appeared in numerous media outlets this fall — including this News & Observer... read more »

Mathematics Department chair Jonathan Mattingly has been awarded the James B. Duke distinguished professorship. Distinguished professorships recognize both exceptional achievement and the potential for future accomplishments. They are awarded to... read more »

DURHAM, N.C. -- On March 26, the U.S. Supreme Court is set to hear a North Carolina lawsuit that could end partisan gerrymandering for good -- and a mode of analysis developed at Duke University could impact their decision. The nation’s highest... read more »

On January 9th, a three-judge court declared North Carolina’s congressional map unconstitutionally gerrymandered, stating that the drawing of the state’s electoral districts gave an advantage to the Republican Party. The US Federal court cited the... read more »

Sayan Mukherjee was named Fellow of the Institute of Mathematical Statistics (IMS) for his significant contributions to mathematical statistics,... read more »