Jonathan Christopher Mattingly

Jonathan Christopher Mattingly
Professor of Mathematics

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.

Current Appointments & Affiliations

Professor of Mathematics, Mathematics, Trinity College of Arts & Sciences 2012
Chair of the Department of Mathematics, Mathematics, Trinity College of Arts & Sciences 2016
Professor of Statistical Science, Statistical Science, Trinity College of Arts & Sciences 2012

Contact Information

Background
Education, Training, & Certifications
- Ph.D., Princeton University 1998
- M.A., Princeton University 1996
- B.S., Yale University 1992
Duke Appointment History
- Associate Professor of Mathematics, Mathematics, Trinity College of Arts & Sciences 2006 - 2012
- Associate Professor, Statistical Science, Trinity College of Arts & Sciences 2008 - 2011
- Assistant Professor of Mathematics, Mathematics, Trinity College of Arts & Sciences 2002 - 2005
Recognition
In the News
- JAN 8, 2018 Duke Research Blog
  
  Jonathan Mattingly: The Mathematics Behind This Week's Gerrymandering Decision
- NOV 28, 2016
  
  Student Team Addresses Gerrymandering With Mathematics
- MAR 18, 2015 USA Today
  
  Duke math professor says odds of a perfect bracket are one in 2.4 trillion
- MAR 18, 2015 Chicago Sun-Times
  
  The odds of a perfect bracket? It's not 1 in 9.2 quintillion
- MAR 17, 2015
  
  News Tip: Realistic Odds of a Perfect NCAA Tournament Bracket
- MAR 17, 2015
  
  The Mathematics of the Perfect Bracket
- NOV 26, 2014 WUNC
  
  Duke mathematicians investigate 2012 election results
- NOV 12, 2014 Greensboro News & Record
  
  Duke study puts Congressional districts under microscope
- OCT 30, 2014 WFAE-Charlotte
  
  Non-political districts would have benefited Democrats in 2012, Duke analysis shows
- OCT 30, 2014
  
  The Week at Duke {in 60 Seconds}: Countdown to Craziness; Political Math
- OCT 29, 2014
  
  Same Votes, Different Districts Would Change Results
Awards & Honors
Expertise
Subject Headings
Research
Selected Grants
- BIGDATA:F: Scalable Bayes uncertainty quantification with guarantees awarded by National Science Foundation 2015 - 2019
- Collaborative research: Propagation of dissipation: Stochastic stabilization in finite and infinite dimensions awarded by National Science Foundation 2016 - 2019
- Analysis and design of robust rare event simulation methods for protein folding and d awarded by University of Chicago 2013 - 2018
- Southeastern Probability Conference 2017: Special Edition Interacting Particle Systems with Applications in Biology, Ecology, and Statistical Physics awarded by National Science Foundation 2017 - 2018
- EMSW21-RTG: awarded by National Science Foundation 2010 - 2017
- Multiscale Analysis of Dynamic Graphs awarded by Office of Naval Research 2012 - 2016
- FRG: Collaborative Proposal: awarded by National Science Foundation 2009 - 2013
- CAREER: Stochastic Analysis and Numerics in Partial Differential Equations and Extended Dynamical Systems awarded by National Science Foundation 2005 - 2011
- Analysis of Mechanisms of Biochemical Homeostasis awarded by National Science Foundation 2006 - 2010
Publications & Artistic Works
Selected Publications
- Conference Papers
  - Mattingly, JC, and Suidan, TM. "Transition measures for the stochastic Burgers equation." 2008. Link to Item
- Journal Articles
  - Hairer, M, and Mattingly, J. "The strong Feller property for singular stochastic PDEs." Annales De L'Institut Henri Poincaré, Probabilités Et Statistiques 54, no. 3 (August 2018): 1314-1340. Full Text Open Access Copy
  - Herschlag, G, Ravier, R, and Mattingly, JC. "Evaluating Partisan Gerrymandering in Wisconsin." (September 2, 2017). Open Access Copy Link to Item
  - Bakhtin, Y, Hurth, T, Lawley, SD, and Mattingly, JC. "Smooth invariant densities for random switching on the torus (Submitted)." (August 1, 2017). Open Access Copy Link to Item
  - Johndrow, JE, and Mattingly, JC. "Coupling and Decoupling to bound an approximating Markov Chain (Submitted)." (July 31, 2017). Open Access Copy Link to Item
  - Glatt-Holtz, NE, Herzog, DP, and Mattingly, JC. "Scaling and Saturation in Infinite-Dimensional Control Problems with Applications to Stochastic Partial Differential Equations." (June 30, 2017). Open Access Copy Link to Item
  - Glatt-Holtz, N, Mattingly, JC, and Richards, G. "On Unique Ergodicity in Nonlinear Stochastic Partial Differential Equations." Journal of Statistical Physics 166, no. 3-4 (February 2017): 618-649. Full Text Open Access Copy
  - Tempkin, JOB, Koten, BV, Mattingly, JC, Dinner, AR, and Weare, J. "Trajectory stratification of stochastic dynamics." (2016). Open Access Copy Link to Item
  - Bakhtin, Y, Hurth, T, and Mattingly, JC. "Regularity of invariant densities for 1D systems with random switching." Nonlinearity 28, no. 11 (October 1, 2015): 3755-3787. Full Text Open Access Copy
  - Herzog, DP, and Mattingly, JC. "A practical criterion for positivity of transition densities." Nonlinearity 28, no. 8 (August 1, 2015): 2823-2845. Full Text Open Access Copy
  - Herzog, D, and Mattingly, J. "Noise-induced stabilization of planar flows II." Electronic Journal of Probability 20, no. 0 (2015). Full Text Open Access Copy
  - Huckemann, S, Mattingly, J, Miller, E, and Nolen, J. "Sticky central limit theorems at isolated hyperbolic planar singularities." Electronic Journal of Probability 20, no. 0 (2015). Full Text Open Access Copy
  - Lawley, SD, Mattingly, JC, and Reed, MC. "Stochastic Switching in Infinite Dimensions with Applications to Random Parabolic PDE." SIAM Journal on Mathematical Analysis 47, no. 4 (January 2015): 3035-3063. Full Text Open Access Copy
  - Luo, S, and Mattingly, JC. "Scaling limits of a model for selection at two scales." (2015). Open Access Copy Link to Item
  - Mattingly, JC, and Pardoux, E. "Invariant measure selection by noise. An example." Discrete and Continuous Dynamical Systems 34, no. 10 (April 2014): 4223-4257. Full Text Open Access Copy
  - Lawley, SD, Mattingly, JC, and Reed, MC. "Sensitivity to switching rates in stochastically switched odes." Communications in Mathematical Sciences 12, no. 7 (2014): 1343-1352. Full Text Open Access Copy
  - Mattingly, JC, and Vaughn, C. "Redistricting and the Will of the People." arXiv preprint arXiv:1410.8796 (2014). (Academic Article) Open Access Copy
  - Hotz, T, Huckemann, S, Le, H, Marron, JS, Mattingly, JC, Miller, E, Nolen, J, Owen, M, Patrangenaru, V, and Skwerer, S. "Sticky central limit theorems on open books." The Annals of Applied Probability 23 (2013): 2238-2258. (Academic Article) Full Text Open Access Copy
  - Luo, S, Reed, M, Mattingly, JC, and Koelle, K. "The impact of host immune status on the within-host and population dynamics of antigenic immune escape." J R Soc Interface 9, no. 75 (October 7, 2012): 2603-2613. Full Text Open Access Copy Link to Item
  - Athreyaz, A, Kolba, T, and Mattingly, JC. "Propagating lyapunov functions to prove noise-induced stabilization." Electronic Journal of Probability 17 (2012). Full Text Open Access Copy
  - Mattingly, JC, McKinley, SA, and Pillai, NS. "Geometric ergodicity of a bead-spring pair with stochastic Stokes forcing." Stochastic Processes and their Applications 122, no. 12 (2012): 3953-3979. Full Text Open Access Copy
  - Porporato, A, Kramer, PR, Cassiani, M, Daly, E, and Mattingly, J. "Local kinetic interpretation of entropy production through reversed diffusion." Phys Rev E Stat Nonlin Soft Matter Phys 84, no. 4 Pt 1 (October 2011): 041142-. Full Text Open Access Copy Link to Item
  - Anderson, DF, and Mattingly, JC. "A weak trapezoidal method for a class of stochastic differential equations." Communications in Mathematical Sciences 9, no. 1 (2011): 301-318. Open Access Copy
  - Hairer, M, Mattingly, JC, and Scheutzow, M. "Asymptotic coupling and a general form of Harris' theorem with applications to stochastic delay equations." Probability Theory and Related Fields 149, no. 1 (2011): 223-259. Full Text Open Access Copy
  - Hairer, M, and Mattingly, JC. "Yet Another Look at Harris' Ergodic Theorem for Markov Chains." SEMINAR ON STOCHASTIC ANALYSIS, RANDOM FIELDS AND APPLICATIONS VI 63 (2011): 109-+. Open Access Copy Link to Item
  - Hairer, M, and Mattingly, JC. "A theory of hypoellipticity and unique ergodicity for semilinear stochastic PDEs." Electronic Journal of Probability 16 (2011): 658-738. Open Access Copy
  - Koelle, K, Ratmann, O, Rasmussen, DA, Pasour, V, and Mattingly, J. "A dimensionless number for understanding the evolutionary dynamics of antigenically variable RNA viruses." Proceedings of the Royal Society B: Biological Sciences 278, no. 1725 (2011): 3723-3730. Full Text Open Access Copy
  - Mattingly, JC, Stuart, AM, and Tretyakov, MV. "Convergence of numerical time-averaging and stationary measures via Poisson equations." SIAM Journal on Numerical Analysis 48, no. 2 (2010): 552-577. Full Text Open Access Copy
  - Hairer, M, and Mattingly, JC. "Slow energy dissipation in anharmonic oscillator chains." Communications on Pure and Applied Mathematics 62, no. 8 (2009): 999-1032. Full Text Open Access Copy
  - Hairer, M, Mattingly, JC, and Martin Hairer, . "Spectral gaps in Wasserstein distances and the 2D stochastic Navier-Stokes equationsSpectral gaps in Wasserstein distances and the 2D stochastic Navier-Stokes equations." Annals of Probability , no. 6 (2008): 993-1032. (Academic Article)
  - Iyer, G, and Mattingly, J. "A stochastic-Lagrangian particle system for the Navier-Stokes equations." Nonlinearity 21, no. 11 (2008): 2537-2553. Full Text
  - Mattingly, J, and Anderson, D. "Propagation of fluctuations in biochemical systems, II: nonlinear chains." IET Systems Biology 1, no. 6 (November 1, 2007): 313-325. Full Text
  - Anderson, DF, Mattingly, JC, Nijhout, HF, and Reed, MC. "Propagation of fluctuations in biochemical systems, I: linear SSC networks." Bull Math Biol 69, no. 6 (August 2007): 1791-1813. Full Text Open Access Copy Link to Item
  - Anderson, DF, Mattingly, JC, Nijhout, HF, and Reed, MC. "Propagation of fluctuations in biochemical systems, I: Linear SSC networks." BULLETIN OF MATHEMATICAL BIOLOGY 69, no. 6 (August 2007): 1791-1813. Full Text Link to Item
  - Bakhtin, Y, and Mattingly, JC. "Malliavin calculus for infinite-dimensional systems with additive noise." Journal of Functional Analysis 249, no. 2 (2007): 307-353. Full Text
  - Lamba, H, Mattingly, JC, and Stuart, AM. "An adaptive Euler-Maruyama scheme for SDEs: Convergence and stability." IMA Journal of Numerical Analysis 27, no. 3 (2007): 479-506. Full Text
  - Mattingly, JC, Suidan, T, and Vanden-Eijnden, E. "Simple systems with anomalous dissipation and energy cascade." Communications in Mathematical Physics 276, no. 1 (2007): 189-220. Full Text
  - Mattingly, JC, Suidan, TM, and Vanden-Eijnden, E. "Anomalous dissipation in a stochastically forced infinite-dimensional system of coupled oscillators." Journal of Statistical Physics 128, no. 5 (2007): 1145-1152. Full Text
  - Nijhout, H, Reed, MC, Anderson, DF, Mattingly, JC, James, SJ, and Ulrich, CM. "Erratum to H. Frederik Nijhout, et al. Epigenetics Volume 1, Issue 2; pp. 81-87." Epigenetics 1, no. 3 (July 2006): 115-115. Full Text
  - Nijhout, HF, Reed, MC, Anderson, DF, Mattingly, JC, James, SJ, and Ulrich, CM. "Long-range allosteric interactions between the folate and methionine cycles stabilize DNA methylation reaction rate." Epigenetics 1, no. 2 (April 2006): 81-87. Link to Item
  - Hairer, M, and Mattingly, JC. "Ergodicity of the 2D Navier-Stokes equations with degenerate stochastic forcing." Annals of Mathematics 164, no. 3 (2006): 993-1032.
  - Mattingly, JC, and Pardoux, É. "Malliavin calculus for the stochastic 2D Navier-Stokes equation." Communications on Pure and Applied Mathematics 59, no. 12 (2006): 1742-1790. Full Text Open Access Copy
  - Bakhtin, Y, and Mattingly, JC. "Stationary solutions of stochastic differential equations with memory and stochastic partial differential equations." Communications in Contemporary Mathematics 7, no. 5 (2005): 553-582. Full Text
  - Mattingly, JC, and Suidan, TM. "The small scales of the stochastic Navier-Stokes equations under rough forcing." JOURNAL OF STATISTICAL PHYSICS 118, no. 1-2 (January 2005): 343-364. Full Text Link to Item
  - Hairer, M, Mattingly, JC, and Pardoux, É. "Malliavin calculus for highly degenerate 2D stochastic Navier–Stokes equations." Comptes Rendus Mathematique 339, no. 11 (December 2004): 793-796. Full Text
  - Hairer, M, and Mattingly, JC. "Ergodic properties of highly degenerate 2D stochastic Navier–Stokes equations." Comptes Rendus Mathematique 339, no. 12 (December 2004): 879-882. Full Text
  - Hairer, M, Mattingly, JC, and Pardoux, E. "Malliavin calculus and ergodic properties of highly degenerate 2D stochastic Navier–Stokes equation." arXiv preprint math/0409057 (2004). (Academic Article)
  - Mattingly, JC, Mattingly, JC, and Mattingly, JC. "On recent progress for the stochastic Navier Stokes equationsOn recent progress for the stochastic Navier Stokes equationsOn Recent Progress for the Stochastic Navier Stokes Equations." Journées "Équations aux Dérivées Partielles" XV (July 2003): viii+298-. (Academic Article) Link to Item
  - Mattingly, JC. "Contractivity and Ergodicity of the Random Map $\boldsymbol{\lowercase{x\,\mapsto\,|x-\theta|}}$." Theory of Probability and Its Applications 47, no. 2 (2003): 333-333. Full Text Open Access Copy
  - Mattingly, JC. "The dissipative scale of the stochastics Navier-Stokes equation: Regularization and analyticity." Journal of Statistical Physics 108, no. 5-6 (December 1, 2002): 1157-1179. Full Text
  - Mattingly, JC. "Exponential convergence for the stochastically forced Navier-Stokes equations and other partially dissipative dynamics." Communications in Mathematical Physics 230, no. 3 (November 1, 2002): 421-462. Full Text
  - Mattingly, JC, Stuart, AM, and Higham, DJ. "Ergodicity for SDEs and approximations: locally Lipschitz vector fields and degenerate noise." Stochastic Processes and Their Applications 101, no. 2 (October 2002): 185-232. Full Text
  - Mattingly, JC, and Mattingly, JC. "Contractivity and ergodicity of the random map $x\mapsto|x-\theta|$." Теория вероятностей и ее применения 47, no. 2 (2002): 388-397. Full Text Open Access Copy
  - Mattingly, JC, and Stuart, AM. "Geometric ergodicity of some hypo-elliptic diffusions for particle motions." Markov Processes and Related Fields 8 (2002): 199-214. (Academic Article)
  - E, W, Mattingly, JC, and Sinai, Y. "Gibbsian Dynamics and Ergodicity¶for the Stochastically Forced Navier–Stokes Equation." Communications in Mathematical Physics 224, no. 1 (November 2001): 83-106. Full Text
  - E, W, and Mattingly, JC. "Ergodicity for the Navier-Stokes equation with degenerate random forcing: Finite-dimensional approximation." Communications on Pure and Applied Mathematics 54, no. 11 (November 2001): 1386-1402. Full Text Open Access Copy
  - Mattingly, JC. "Ergodicity of 2D Navier-Stokes Equations with¶Random Forcing and Large Viscosity." Communications in Mathematical Physics 206, no. 2 (October 1, 1999): 273-288. Full Text
  - Mattingly, JC, and Sinai, YG. "An elementary proof of the existence and uniqueness theorem for the Navier-Stokes equations." Communications in Contemporary Mathematics 1, no. 4 (1999): 497-516. Open Access Copy
  - Holmes, PJ, Lumley, JL, Berkooz, G, Mattingly, JC, and Wittenberg, RW. "Low-dimensional models of coherent structures in turbulence." Physics Reports 287, no. 4 (August 1997): 337-384. Full Text
  - Bangia, S, Graves, CV, Herschlag, G, Kang, HS, Luo, J, Mattingly, JC, and Ravier, R. "Redistricting: Drawing the Line." Open Access Copy Link to Item
  - Cooke, B, Herzog, DP, Mattingly, JC, McKinley, SA, and Schmidler, SC. "Geometric Ergodicity of Two--dimensional Hamiltonian systems with a Lennard--Jones--like Repulsive Potential." Open Access Copy Link to Item
  - Gao, Y, Kirkpatrick, K, Marzuola, J, Mattingly, J, and Newhall, K. "Limiting Behaviors of High Dimensional Stochastic Spin Ensembles." . Open Access Copy Link to Item
  - Herschlag, G, Kang, HS, Luo, J, Graves, CV, Bangia, S, Ravier, R, and Mattingly, JC. "Quantifying Gerrymandering in North Carolina." Link to Item
  - Herzog, DP, and Mattingly, JC. "Ergodicity and Lyapunov functions for Langevin dynamics with singular potentials." Open Access Copy Link to Item
  - Heymann, M, Teitsworth, SW, and Mattingly, JC. "Rare Transition Events in Nonequilibrium Systems with State-Dependent Noise: Application to Stochastic Current Switching in Semiconductor Superlattices." Open Access Copy Link to Item
  - Johndrow, JE, Mattingly, JC, Mukherjee, S, and Dunson, D. "Optimal approximating Markov chains for Bayesian inference." Open Access Copy Link to Item
  - Johndrow, JE, and Mattingly, JC. "Error bounds for Approximations of Markov chains." Open Access Copy Link to Item
  - Mattingly, JC, Pillai, NS, and Stuart, AM. "Diffusion limits of the random walk Metropolis algorithm in high dimensions." Annals of Applied Probability 22, no. 3: 881-930. Full Text Open Access Copy Link to Item
  - Munch, E, Turner, K, Bendich, P, Mukherjee, S, Mattingly, J, and Harer, J. "Probabilistic Fréchet Means for Time Varying Persistence Diagrams." Full Text Open Access Copy Link to Item
  - Wang, C, Mattingly, J, and Lu, YM. "Scaling Limit: Exact and Tractable Analysis of Online Learning Algorithms with Applications to Regularized Regression and PCA." . Link to Item
- Other Articles
  - Holmes, PJ, Mattingly, JC, and Wittenberg, RW. "Low-dimensional models of turbulence or, The dynamics of coherent structures." 19 (2001): 177-215. Full Text
Teaching & Mentoring
Recent Courses
Scholarly, Clinical, & Service Activities
Presentations & Appearances
Outreach & Engaged Scholarship
- Bass Connections Faculty Team Member. Data+. June 2016 - July 2016 2016
- Bass Connections Faculty Team Member . Data+. June 2015 - August 2016 2015 - 2016
Service to the Profession

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Education, Training, & Certifications

Duke Appointment History

In the News

Awards & Honors

Subject Headings

Selected Grants

Selected Publications

Conference Papers

Journal Articles

Other Articles

Recent Courses

Presentations & Appearances

Outreach & Engaged Scholarship

Service to the Profession