## Emiliano De Simone

**Ph.D., Researcher**

**Email:** firstname.lastname(at)helsinki.fi

**Personal Homepage:**

**Telephone:** +358 9 191 51528

**Facsimile:** (Departmental)

**Mailing Address:**

Department of Mathematics and Statistics

P.O. Box 68

FIN-00014 University of Helsinki

Finland

**Visiting Address:**

Gustaf Hällströmin katu 2 b, Helsinki

Room B421

### Scientific Activities:

My main field of research so far has been classical Hamiltonian dynamics, in particular KAM theory. KAM theory consists of a number of methods and techniques which have been developed in order to solve certain stability problems that typically arise in the frame of classical Hamiltonian dynamics. For an introduction to KAM theory see, for example, "Mathematical methods of classical mechanics" by V.I. Arnold, appendix 8.

In (1),(2),(3),(4), in order to prove the classical KAM theorem, I used a scheme based on the Renormalization Group (RG) of Quantum Field Theory, whose use in KAM theory has been introduced by Gallavotti, Gentile et al. and further developed in "KAM Theorem and Quantum Field Theory" by Bricmont, Gawedzki and Kupiainen.

In (3), following the scheme adopted in the latter paper, I was able to extend its application to the case of a finitelly many times differentiable perturbation (when the so called Lindstedt Series is not convergent).

In (4), with Antti Kupiainen, we gave another RG proof of the KAM theorem in the case of an analytic perturbation, using continuous renormalization scales instead of discrete ones, which ends up in solving a simple evolution PDE with quadratic nonlinearity. This equation is well known in QFT where it goes under the name of Polchinski equation.

I got my degree in mathematics in July 2001 from the University of Rome "Roma III", under the supervision of Prof. Luigi Chierchia with the Master thesis ("Tesi di laurea") (1)

I attained my Ph.D. in mathematics in May 2006 at the University of Helsinki under the supervision of Prof. Antti Kupiainen, with the final dissertation (2).

### Publications and other things

(1) Master thesis: E. De Simone * "Teoria KAM e Gruppo di Rinormalizzazione"* (.ps).

(2) Ph.D. Dissertation: E. De Simone * "Renormalization methods in KAM theory"* (.pdf)

(3) E.De Simone * "A renormalization proof of the KAM theorem for non-analytic perturbation"* (.pdf) (2007)

*Reviews in Mathematical Physics Vol. 19, No. 6(2007)1-37*.

(4) E. De Simone, A.Kupiainen * "KAM Theorem and renormalization group"* Submitted for pubblication to

*Ergodic Theory and Dynamical Systems*.