Math @ Duke

Jonathan C. Mattingly, Professor of Mathematics and Statistical Science and Chair
 Contact Info:
 Office Hours:
 TBA
 Education:
Ph.D.  Princeton University  1998 
M.A.  Princeton University  1996 
Auditor  ENS Lyon  1993 
B.S.  Yale University  1992 
High School Diploma  NCSSM  1988 
 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)
 Mattingly, JC; Pardoux, E, Invariant measure selection by noise. An example,
Discrete and Continuous Dynamical Systems, vol. 34 no. 10
(2014),
pp. 42234257, ISSN 10780947 [arXiv:1403.3593], [repository], [doi] [abs]
 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. 22382258, ISSN 10505164 [arXiv:1202.4267], [12AAP899], [doi] [abs]
 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. 881930 [1003.4306], [1003.4306v4], [doi] [abs]
 with Martin Hairer, Yet another look at Harris' ergodic theorem for Markov chains
(August, 2008) [arXiv:0810.2777] [abs]
 with David P. Herzog, NoiseInduced Stabilization of Planar Flows II
(Submitted, April, 2014) [arXiv:1404.0955]
 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. 301318, ISSN 15396746 [0906.3475], [repository] [abs]
 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. 658738, ISSN 10836489 [arXiv:0808.1361], [repository] [abs]
 with Hairer, M; Mattingly, JC; Martin Hairer, , Spectral gaps in Wasserstein distances and the 2D stochastic NavierStokes equationsSpectral gaps in Wasserstein distances and the 2D stochastic NavierStokes equations,
Annals of Probability no. 6
(2008),
pp. 9931032 [MR2478676], [math.PR/0602479] [abs]
 with David P. Herzog, NoiseInduced Stabilization of Planar Flows I
(Submitted, April, 2014) [arXiv:1404.0957]
 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. 223259, ISSN 01788051 [MR2531551], [0902.4495], [repository], [doi] [abs]
 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. 37553787, ISSN 09517715 [arXiv:1406.5425], [repository], [doi] [abs]
 Hairer, M; Mattingly, JC, Slow energy dissipation in anharmonic oscillator chains,
Communications on Pure & Applied Mathematics, vol. 62 no. 8
(2008),
pp. 9991032, ISSN 00103640 [MR2531551], [arXiv:0712.3884], [doi] [abs]
 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]
 with Mattingly, JC; Stuart, AM; Tretyakov, MV, Convergence of numerical timeaveraging and stationary measures via Poisson equations,
SIAM Journal on Numerical Analysis, vol. 48 no. 2
(2010),
pp. 552577, ISSN 00361429 [MR2669996], [0908.4450], [repository], [doi] [abs]
 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. 185232, ISSN 03044149 [MR2003i:60103], [pdf], [doi] [abs]
 with Mattingly, JC; Vaughn, C, Redistricting and the Will of the People
(Preprint, October, 2014) [1410.8796v1] [abs]
 Mattingly, JC; Pardoux, É, Malliavin calculus for the stochastic 2D NavierStokes equation,
Communications on Pure & Applied Mathematics, vol. 59 no. 12
(December, 2006),
pp. 17421790, ISSN 00103640 [math.PR/0407215], [doi] [abs]
 Mattingly, JC, Exponential convergence for the stochastically forced NavierStokes equations and other partially dissipative dynamics,
Communications in Mathematical Physics, vol. 230 no. 3
(November, 2002),
pp. 421462, ISSN 00103616 [MR2004a:76039], [pdf], [doi] [abs]
 Hairer, M; Mattingly, JC, Ergodicity of the 2D NavierStokes equations with degenerate stochastic forcing,
Annals of Mathematics, vol. 164 no. 3
(November, 2006),
pp. 9931032, ISSN 0003486X [math.PR/0406087] [abs]
 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. 83106, ISSN 00103616 (Dedicated to Joel L. Lebowitz.) [MR2002m:76024], [pdf], [doi]
 Recent Grant Support
 BIGDATA:F: Scalable Bayes uncertainty quantification with guarantees, National Science Foundation, 1546130, 2015/112019/10.
 Collaborative research: Propagation of dissipation: Stochastic stabilization in finite and infinite dimensions, National Science Foundation, 1613337, 2016/062019/05.
 Analysis and design of robust rare event simulation methods for protein folding and d, University of Chicago, FP055408, 2013/082018/07.
 Southeastern Probability Conference 2017: Special Edition Interacting Particle Systems with Applications in Biology, Ecology, and Statistical Physics, National Science Foundation, DMS1719189, 2017/052018/04.
 EMSW21RTG:, National Science Foundation, DMS0943760, 2010/092017/08.
 Multiscale Analysis of Dynamic Graphs, Office of Naval Research, N00014121060101, 2012/082016/07.
 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


dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821
 
Mathematics Department
Duke University, Box 90320
Durham, NC 277080320

