People at CTMS

» Search People

Jonathan C. Mattingly, Professor of Mathematics and Statistical Science and Chair of Mathematics

 

Jonathan C. Mattingly

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.

Contact Info:
Office Location:  297 Physics
Office Phone:  (919) 660-6978
Email Address: send me a message
Web Page:  http://www.math.duke.edu/~jonm

Education:

Ph.D.Princeton University1998
M.A.Princeton University1996
AuditorENS Lyon1993
B.S.Yale University1992
High School DiplomaNCSSM1988

Specialties:

Probability
Applied Math
Analysis
Mathematical Physics

Research Interests: Applied mathematics, Probability, Ergodic Theory, Stochastic partial differential equations, Stochastic dynamical systems, Stochastic Numerical methods, Fluids

Keywords:

Differential equations, Nonlinear • Ergodic theory • Evolution • Fluid mechanics • Folic Acid • Invariant measures • Lyapunov functions • Malliavin calculus • Mixing • Models, Biological • Nonequilibrium statistical mechanics • Nonlinear Dynamics • Probability Theory • Random dynamical systems • Stochastic analysis • Stochastic differential equations • Stochastic partial differential equations • Stochastic Processes • Turbulence

Curriculum Vitae

Current Ph.D. Students   (Former Students)

    Postdocs Mentored
    • Herzog David (August, 2011 - June, 2013)  
    • Avanti Athreya (2009 - 2011)  
    • Oliver Diaz Espinosa (2009 - 2011)  
    • Matthias Heymann (September, 2007 - August, 2010)  
    • Boumediene Hamzi (September, 2007 - June, 2010)  
    • Scott McKinley (September 1, 2006 - June 1, 2010)  
    • David Anderson (September, 2005 - December, 2005)  
    • Yuri Bakhtin (2004)  

    Undergraduate Researches Supervised
    • (Paul) Yang Ziquan (June, 2013 - 2014)  
    • Steve Siyang Wang (June, 2013 - November, 2013)  
    • Christy Vaughn (January, 2013 - 2015)  

    Representative Publications   (More Publications)

    1. Mattingly, JC; Pardoux, E, Invariant measure selection by noise. An example, Discrete and Continuous Dynamical Systems, vol. 34 no. 10 (2014), pp. 4223-4257, ISSN 1078-0947 [arXiv:1403.3593], [repository], [doi]  [abs]
    2. Hotz, T; Huckemann, S; Le, H; Marron, JS; Mattingly, JC; Miller, E; Nolen, J; Owen, M; Patrangenaru, V; Skwerer, S, Sticky central limit theorems on open books, The annals of applied probability : an official journal of the Institute of Mathematical Statistics, vol. 23 no. 6 (2013), pp. 2238-2258, ISSN 1050-5164 [arXiv:1202.4267], [12-AAP899], [doi]  [abs]
    3. with Mattingly, JC; Pillai, NS; Stuart, AM, Diffusion limits of the random walk Metropolis algorithm in high dimensions, Annals of Applied Probability, vol. 22 no. 3 (June, 2011), pp. 881-930 [1003.4306], [1003.4306v4], [doi]  [abs]
    4. with Martin Hairer, Yet another look at Harris' ergodic theorem for Markov chains (August, 2008) [arXiv:0810.2777]  [abs]
    5. with David P. Herzog, Noise-Induced Stabilization of Planar Flows II (Submitted, April, 2014) [arXiv:1404.0955]
    6. with Anderson, DF; Mattingly, JC, A weak trapezoidal method for a class of stochastic differential equations, Communications in Mathematical Sciences, vol. 9 no. 1 (March, 2011), pp. 301-318, ISSN 1539-6746 [0906.3475], [repository]  [abs]
    7. with Hairer, M; Mattingly, JC, A theory of hypoellipticity and unique ergodicity for semilinear stochastic PDEs, Electronic Journal of Probability, vol. 16 no. 23 (2011), pp. 658-738, ISSN 1083-6489 [arXiv:0808.1361], [repository]  [abs]
    8. with Hairer, M; Mattingly, JC; 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), pp. 993-1032 [MR2478676], [math.PR/0602479]  [abs]
    9. with David P. Herzog, Noise-Induced Stabilization of Planar Flows I (Submitted, April, 2014) [arXiv:1404.0957]
    10. with Hairer, M; Mattingly, JC; Scheutzow, M, Asymptotic coupling and a general form of Harris' theorem with applications to stochastic delay equations, Probability Theory and Related Fields, vol. 149 no. 1 (2011), pp. 223-259, ISSN 0178-8051 [MR2531551], [0902.4495], [repository], [doi]  [abs]
    11. with Bakhtin, Y; Hurth, T; Mattingly, JC, Regularity of invariant densities for 1D systems with random switching, Nonlinearity, vol. 28 no. 11 (October, Submitted, 2015), pp. 3755-3787, ISSN 0951-7715 [arXiv:1406.5425], [repository], [doi]  [abs]
    12. Hairer, M; Mattingly, JC, Slow energy dissipation in anharmonic oscillator chains, Communications on Pure & Applied Mathematics, vol. 62 no. 8 (2008), pp. 999-1032, ISSN 0010-3640 [MR2531551], [arXiv:0712.3884], [doi]  [abs]
    13. with Sean D. Lawley and Michael C. Reed, Stochastic switching in infinite dimensions with applications to random parabolic PDEs (Submitted, 2014) [arXiv:1407.2264]  [abs]
    14. with Mattingly, JC; Stuart, AM; Tretyakov, MV, Convergence of numerical time-averaging and stationary measures via Poisson equations, SIAM Journal on Numerical Analysis, vol. 48 no. 2 (2010), pp. 552-577, ISSN 0036-1429 [MR2669996], [0908.4450], [repository], [doi]  [abs]
    15. Mattingly, JC; Stuart, AM; Higham, DJ, Ergodicity for SDEs and approximations: locally Lipschitz vector fields and degenerate noise, Stochastic Processes and their Applications, vol. 101 no. 2 (October, 2002), pp. 185-232, ISSN 0304-4149 [MR2003i:60103], [pdf], [doi]  [abs]
    16. with Mattingly, JC; Vaughn, C, Redistricting and the Will of the People (Preprint, October, 2014) [1410.8796v1]  [abs]
    17. Mattingly, JC; Pardoux, É, Malliavin calculus for the stochastic 2D Navier-Stokes equation, Communications on Pure & Applied Mathematics, vol. 59 no. 12 (December, 2006), pp. 1742-1790, ISSN 0010-3640 [math.PR/0407215], [doi]  [abs]
    18. Mattingly, JC, Exponential convergence for the stochastically forced Navier-Stokes equations and other partially dissipative dynamics, Communications in Mathematical Physics, vol. 230 no. 3 (November, 2002), pp. 421-462, ISSN 0010-3616 [MR2004a:76039], [pdf], [doi]  [abs]
    19. Hairer, M; Mattingly, JC, Ergodicity of the 2D Navier-Stokes equations with degenerate stochastic forcing, Annals of Mathematics, vol. 164 no. 3 (November, 2006), pp. 993-1032, ISSN 0003-486X [math.PR/0406087]  [abs]
    20. E, W; Mattingly, JC; Sinai, Y, Gibbsian Dynamics and Ergodicity¶for the Stochastically Forced Navier–Stokes Equation, Communications in Mathematical Physics, vol. 224 no. 1 (November, 2001), pp. 83-106, ISSN 0010-3616 (Dedicated to Joel L. Lebowitz.) [MR2002m:76024], [pdf], [doi]