# Fraydoun Rezakhanlou

**Email address:** rezakhan@math.berkeley.edu

**Postal Address:**
- Department of Mathematics
- University of California
- Berkeley, CA, 94720-3840

### Teaching:

Spring 2019: Math C223B,
Advanced Topics in Probablity and Stochastic Processes
Fall 2018: Math 278, Weak KAM Theory and Symplectic Topology
Spring 2018: Math 219, Dynamical Systems
Spring 2017: Math 118, Fourier Analysis, Wavelets, and Signal Processing
Spring 2017: Math 140, Metric Differential Geometry
Fall 2015: Math 242, Symplectic Geometry

### Recent papers:

Scaling Limit of Small Random Perturbation of Dynamical Systems (with Insuk Seo).

Stochastic Solutions to Hamilton-Jacobi 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 Linéaire, 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. Notes for an advanced
graduate course on ''Symplectic Geometry''

Lectures on Dynamical Systems, part I , part II .
Notes for an advanced graduate course on "Dynamical Systems".

Lectures on Random Matrices.

Hamiltonian ODE, Homogenization, and Symplectic Topology.

Lectures on Large Deviation Principle.

### Slides:

Equilibrium Fluctuations for Coagulating-Fragmenting Brownian Particles.

Coagulating Brownian Particles, Gelation and Smoluchowski Equation