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

Jonathan C. Mattingly
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

Teaching (Fall 2016):

  • MATH 790-90.03, MINICOURSE IN ADVANCED TOPICS Synopsis
    Physics 205, TuTh 01:25 PM-02:40 PM
Teaching (Spring 2017):

  • MATH 545.01, STOCHASTIC CALCULUS Synopsis
    Physics 235, TuTh 01:25 PM-02:40 PM
Office Hours:

TBA
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

Areas of Interest:

Ergodic theory
Truly infinite dimensional behabior in SPDEs
Scaling limited of algorithems used in simulation and data analysis
Probabilistic algorithms for large data
Stabilization of dynamics my noise
scaling limits of stochastic algorithms

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 Research 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 Martin Hairer, Yet another look at Harris' ergodic theorem for Markov chains (August, 2008) [arXiv:0810.2777]  [abs]
    4. with David P. Herzog, Noise-Induced Stabilization of Planar Flows II (Submitted, April, 2014) [arXiv:1404.0955]
    5. 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]
    6. 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]
    7. 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]
    8. with David P. Herzog, Noise-Induced Stabilization of Planar Flows I (Submitted, April, 2014) [arXiv:1404.0957]
    9. 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]
    10. 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]
    11. 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]
    12. 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]
    13. 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]
    14. 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]
    15. 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]
    16. 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]
    17. 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]
    18. 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]
    Recent Grant Support

    • BIGDATA:F: Scalable Bayes uncertainty quantification with guarantees, National Science Foundation, 1546130, 2015/11-2019/10.      
    • Collaborative research: Propagation of dissipation: Stochastic stabilization in finite and infinite dimensions, National Science Foundation, 1613337, 2016/06-2019/05.      
    • Analysis and design of robust rare event simulation methods for protein folding and d, University of Chicago, FP055408, 2013/08-2018/07.      
    • EMSW21-RTG:, National Science Foundation, DMS-0943760, 2010/09-2017/08.      
    • Multiscale Analysis of Dynamic Graphs, Office of Naval Research, N00014-12-1-0601-01, 2012/08-2016/07.      
    • MULTISCALE ANALYSIS OF DYNAMIC GRAPHS, Office of Naval Research, N000141210601, 2012/04.      
    • Visitinig Member, Institut Universitaire de France, 2004/05.      
    Conferences Organized

    • Organized invited session at SPA2013. August 2013, Organized invited session at SPA2013, August, 2013  
    • Co Organizer (with Amarjit Budhiraja ) : Seminar on Stochastic Processes 2013. March 2013, Co Organizer (with Amarjit Budhiraja ) : Seminar on Stochastic Processes 2013, March, 2013  
    • Local Orgnaizer (with Rick Durrett) : Woman in Probability III. October 2012, Local Orgnaizer (with Rick Durrett) : Woman in Probability III, October, 2012  
    • SAMSI Stochastic Dynamics tradition workshop. November 2010, SAMSI Stochastic Dynamics tradition workshop, November, 2010  
    • MFO week long school on ergodic theory. October 2010, MFO week long school on ergodic theory, October, 2010  
    • local liaison/Organizer SAMSI year on stochastic dynamics. 2009 - 2010, local liaison/Organizer SAMSI year on stochastic dynamics, 2009 - 2010  
    • SAMSI Opening Workshop for Stochastic Dynamics. August 2009, SAMSI Opening Workshop for Stochastic Dynamics, August, 2009  
    • AIM conference: Stochastic numerics methods and application, October, 2007  
    • Organizer MSRI semster program, December 30, 2006 - May 30, 2007  
    • MSRI: Mathematical Issues in Stochastic Approaches for Multiscale Modeling, May 21, 2007 - May 26, 2007  
    • Minisymposium, SIAM dynamical systems meeting, May, 2007  
    • MSRI: Stochastic Dynamical Systems and Control, March 26, 2007 - February 30, 2007  

     

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