Fraydoun Rezakhanlou

Email address: rezakhan@math.berkeley.edu

Postal Address:

Teaching:

  • Fall 2024: Math 219, Dynamical Systems

  • Spring 2024: Math 270, Topics in Symplectic Geometry

  • Spring 2024: Math 290, Topics in Dynamical Systems

  • Fall 2023: Math 242, Symplectic Geometry

  • Fall 2022: Math 224, Mathematical Methods for the Physical Sciences

  • Fall 2021: Math 279, Stochastic PDEs

  • Fall 2021: Math 121A, Mathematical Tools for the Physical Sciences

  • Spring 2019: Math C223B, Advanced Topics in Probablity and Stochastic Processes

  • Fall 2018: Math 278, Weak KAM Theory and Symplectic Topology

  • Spring 2017: Math 118, Fourier Analysis, Wavelets, and Signal Processing

  • Spring 2017: Math 140, Metric Differential Geometry


  • Recent papers:

    The random Arnold Conjecture: a new probabilistic Conley-Zehnder Theory for symplectic maps (with Alvaro Pelayo), to appear in Commun. Math. Phys.

    Kinetic Description of Scalar Conservation Laws with Markovian Data

    A Kinetic Approach to Burgers Equation with White Noise Initial Data (with Mehdi Ouaki)

    Hamiltonian ODE, Homogenization, and Symplectic Topology , to appear in volume 72 of MSRI Book Series.

    Scaling Limit of Small Random Perturbation of Dynamical Systems (with Insuk Seo), Ann. Inst. H. Poincare-Probabilites et Statistiques, vol 59, 869--903 (2023)

    Random Tessellations and Gibbsian Solutions of Hamilton-Jacobi Equations (with Mehdi Ouaki)Commun. Math. Phys. vol 394, 409--470 (2022).

    Kinetic statistics of scalar conservation laws with piecewise-deterministic Markov process data (with Dave Kaspar) Arch. Rational Mech. Anal. Volume 1, 259--298 (2020).

    Stochastic Solutions to Hamilton-Jacobi Equations . In ``Stochastic Dynamics Out of Equilibrium,'' Springer Proceedings in Mathematics and Statistics, Volume 282, 206-238 (2019).

    Metastability of Zero Range Processes via Poisson Equations

    Optimal Transport Problems For Contact Structures .

    Regular Flows for Diffusions with Rough Drifts .

    The Poincare--Birkhoff Theorem in Random Dynamics (with A. Pelayo) Trans. Amer. Math. Soc. Volume 370, 601-639 (2018).

    Scalar conservation laws with monotone pure-jump Markov initial conditions (with Dave Kaspar) Probab. Theory and Related Fields. volume 165, 867-899 (2016).

    Stochastically Symplectic Maps and Their Applications to Navier-Stokes Equation . Ann. Inst. H. Poincare-Anal. Non Lineaire, Volume 33, 1--22 (2016).

    Pointwise Bounds for the Solutions of the Smoluchowski Equation with Diffusion,. Arch. Rational Mech. Anal. 212, 1011--1035 (2014).

    Gelation for Marcus-Lushnikov Process. This paper (without Section 5) appeared in Annals of Probability, Volume 41, 1806-1830 (2013).

    Moment Bounds for the Solutions of the Smoluchowski Equation with Coagulation and Fragmentation, Proceedings of the Royal Society of Edinburgh, Volume 140A, 1041-1059 (2010)

    A Prelude to the Theory of Random Walks in Random Environments, Bulletin of IMS, Volume 37, No. 2, 5-20 (2011).

    Equilibrium Fluctuations for a Model of Coagulating-Fragmenting planar Brownian Particles, Commun. Math. Phys. Volume 296, 769-826, (2010)

    Coagulation, Diffusion and the Continuous Smoluchowski Equation, Stochastic Process. Appl. Volume 119, 3042-3080 , (2009)

    Moment bounds for the Smoluchowski equation and their consequences, Commun. Math. Phys. Volume 276, 645-670, (2007)

    The kinetic limit of a system of coagulating Brownian particles (with Alan Hammond) Arch. Rational Mech. Anal. Volume 185, 1-67, (2007)

    Boltzmann-Grad limits for stochastic hard sphere models Comm. Math. Phys. Volume 284, 555-637 (2004)


    Lecture notes:

    Lectures on Symplectic Geometry.

    Lectures on Dynamical Systems, part I , part II .

    Lectures on Random Matrices.

    Hamiltonian ODE, Homogenization, and Symplectic Topology.

    Lectures on Large Deviation Principle.

    Stochastic Growth and KPZ Equation.

    Stochastic PDE.

    Mathematical Methods in Physical Sciences.

    Growth Models and Hamilton-Jacobi PDEs.


    Slides:

    Equilibrium Fluctuations for Coagulating-Fragmenting Brownian Particles.


    Coagulating Brownian Particles, Gelation and Smoluchowski Equation


    Kinetic Theory for Hamiton-Jacobi PDE


    Kinetic Description for Hamilton-Jacobi Equation: Part I, Part II, Part III, Part IV,



    Editorial Board:

    Pacific Rim Conference in Mathematics:

  • The Eighth Pacific Rim Conference in Mathematics was held at the U.C. Berkeley from Monday 3th August to Friday 7th August 2020.