Ecole Normale Supérieure
CERES-ERTI
Centre d'Enseignement et de Recherches sur l'Environnement et la Societé
Environmental Research and Teaching Institute
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Mickaël D. Chekroun
E-mail: 'c''h''e''k''r''o''@''l''m''d''.''e''n''s''.''f''r'
Visiting address: Ecole Normale Supérieure
CERES-ERTI
Room R14-2 (level 0)
24 rue Lhomond / 8 rue Erasme
75005 Paris
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Fax: +33 1 44 32 27 27
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Research interests

  • Deterministic dynamical systems - Diffeomorphisms group and conjugacy problems. Topological equivalence of flows and diffeomorphisms. Averaging methods in ordinary and partial differential equations. Infinite dimensional dissipative dynamical systems.
  • Random dynamical systems - Stochastic (partial) differential equations and random attractors. Applications to climate dynamics and mathematical ecology.
  • Population dynamics and mathematical ecology - Effect of environmental heterogeneity on population resilience to external perturbations. Role of chaos in biodiversity.
  • Geophysical fluid dynamics and climate dynamics - Application of dynamical systems theory to climate dynamics. Low-frequency variability of wind-driven ocean circulation.

    • Teaching

  • Atelier "Modelisation: reserves marines" (Workshop "Modelling: marine reserves")
  • Introduction to bifurcation theory and application to mathematical ecology.

    • Publications by topics

    Infinite-dimensional evolution equations

  • M.D. Chekroun, F. Di Plinio, and N.E. Glatt-Holtz, (2009). Random attractor of stochastic Navier-Stokes equations with memory, in preparation.
  • M.D. Chekroun, F. Di Plinio, N.E. Glatt-Holtz, and V. Pata (2009). Asymptotics of the Coleman-Gurtin model. Discrete and Continuous Dynamical Systems, Series S, in press.
  • L. Roques and M.D. Chekroun (2007). On Population Resilience to External Perturbations. SIAM Journal on Applied Mathematics, Vol. 68, No. 1, pp. 133--153, 2007.
  • M.D. Chekroun and L.J. Roques (2006). Models of population dynamics under the influence of external perturbations: mathematical results, C. R. Acad. Sci. Paris, Ser. I, 343: 307-310.

    • Applications to climate dynamics and mathematical ecology

  • M.D. Chekroun, E. Simonnet, and M. Ghil (2009). Stochastic climate dynamics: Random attractors and time-dependent invariant measures, submitted.
  • L.Roques, and M.D. Chekroun (2009). Probing chaos and biodiversity in the "simplest" Lotka-Volterra competition model, submitted.
  • L.Roques, and M.D. Chekroun (2009). Does reaction-diffusion support the duality of fragmentation effect?, Ecological Complexity, in press.
  • M. Ghil, M.D. Chekroun, and E. Simonnet (2008). Climate dynamics and fluid mechanics: Natural variability and related uncertainties, Invited survey paper for Special Issue on The Euler Equations: 250 Years On, Physica D: Nonlinear phenomena, 237, 2111--2126.

    • Dynamical systems

  • M.D. Chekroun, J. Roux and M. Ghil (2009). Homeomorphism groups of normed vector spaces: The conjugacy problem and the Koopman operator, submitted.
  • M.D. Chekroun, M. Ghil, J. Roux and F. Varadi (2006). Averaging of time-periodic systems without a small parameter. Discrete and Continuous Dynamical Systems (DCDS A) 14(4):753-782.


    • Special events

  • European Geosiences Union, General Assembly 2009, Vienna, Austria, 19-24 Apr. 2009, Co-convener, with M. Ghil and E. Simonnet, of the special session "Chaotic and Stochastic Climate Dynamics", co-listed Climate:Past, Present, Future and Nonlinear Processes in Geophysics (CL55/NP8)
  • Summer School on "Climate variability & Climate Change: Estimating and Reducing Uncertainties", 8-17 June 2009, Visegrad, Hungary, Lecture on:"An Introduction to Random Dynamical Systems".
  • American Mathematical Society, Baylor University in Waco, Texas, October 16-18, 2009, Co-convener, with Shouhong Wang and Nathan Glatt-Holtz (Indiana University), special session on "Nonlinear and Stochastic Partial Differential Equations", deadline for abstract submission: August 25, 2009.

    • Miscellaneous

  • D. Kondrashov, M.D. Chekroun, S. Kravtsov, and M. Ghil (2009), Random attractor reconstruction by empirical model reduction: Application to ENSO time series, Poster presented at EGU, General Assembly, 2009.
  • E. Simonnet, M.D. Chekroun, and M. Ghil, (2008), A Stochastic Nonlinear Model of El Nino: Random Dynamical Systems and Predictability, Poster presented at EGU, General Assembly, 2008.
  • M.D. Chekroun (2008), A Note on Existence of Random Attractors, essai.
  • I. Ciril, M.D. Chekroun, and L. Roques,(2007) On performing accurate Bayesian estimation using set theoretic framework. Application to Kalman filter under general convex constraints. Preprint.
  • M.D. Chekroun, J. Darbon, and I. Ciril (2006) On a polynomial vector field model for shape representation, Lecture Note in Computer Science 4142, A. Campilho and M. Kamel (Eds.): Image Analysis and Recognition (ICIAR) 2006, pp. 386--397, Springer-Verlag.




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