Although this may seem a paradox, all exact science is dominated by the idea of approximation.
by Russell, Bertrand (1872-1970)

Geometry and Physics XII, Hainan (China), 10-14/03/2014

Next year I’ll come to Sanya, Hainan, China to attend “GAP XII”, an international conference on geometry and physics.

The organizers said they would have money to cover local expenses for a number of participants, so if anyone is interested in visiting Sanya, please contact them (or contact me if you don’t know them)

. . . → Read More: Geometry and Physics XII, Hainan (China), 10-14/03/2014

Death to supersymmetry?!

http://www.bbc.co.uk/news/science-environment-20300100

Will have to try to understand what does it mean

Dynamical Systems (5): Ergodicity

These are  the notes that i’m trying to write up for the 5th lecture of my doctoral course “Basic principles of dynamical systems” in Toulouse. This lecture is about ergodicity.

I’m behind schedule in many things, so please be patient with me. The correct lecture notes will appear one day. I’m even planning to . . . → Read More: Dynamical Systems (5): Ergodicity

Toán tài chính: các bài giảng trường hè và hội nghị 2012

Lecture Notes in Mathematical Finance (links to the files)

Link đến các files bài giảng

Trường hè (Đại học kinh tế – luật & Trung tâm JVN):

Phạm Huyên, Stochastic Optimal Control in Finance

Luciano Campi, Pricing and Hedging in Energy Market

Mathieu Rosenbaum, High Frequency Trading: Part 1, Part 2, Part 3

Hội . . . → Read More: Toán tài chính: các bài giảng trường hè và hội nghị 2012

Boycotting Elsevier: let’s join the efforts of our scientific community!

Below is a very interesting letter from Arieh Iserles about why should we boycott Elsevier:

—– I strongly encourage you to read the very recent posting of Doug Arnold on the IMU Journals’ blog, http://blog.mathunion.org/journals/ . Also, more humbly, my posting on Tim Gowers’s blog, Coming late to this discussion (but not to the issue . . . → Read More: Boycotting Elsevier: let’s join the efforts of our scientific community!

Formal non-integrability of resonant systems

I’m coming back here to an old but still open (as far as I know) problem:

Show that a generic Hamiltonian system with a fixed point and whose resonance degree at that point is at least 2 is not formally integrable.

Recall that, if the system is non-resonant then it’s formally integrable due to . . . → Read More: Formal non-integrability of resonant systems

Stochastic Control and Optimal Stopping in Finance (Toulouse 12/2011)

Last updated: 09/12/2011

This is a brief real-time report on the conference OSIF (Toulouse 1, 08-09/Dec/2011)

About 40+ participants. Some are my students Lunchs and coffees  are served at the conference free of charge for the participants :-). The organizers are A. Blanchet & S. Villeneuve (my colleagues at Toulouse 1)

Thursday:

9h30: Goran . . . → Read More: Stochastic Control and Optimal Stopping in Finance (Toulouse 12/2011)

Exercices d’algèbre linéaire (DM3/2011)

(Devoir Maison No. 3, Licence 2 en Mathématiques, Novembre 2011)

Exercice 1. (Somme de carrés des coefficients). Soit un espace euclidien de dimension , et soit .

1) Montrer que, si et sont deux bases orthonormales de , alors

En déduire que la quantité est indépendante de la base orthonormale choisie.

(Indication: utiliser . . . → Read More: Exercices d’algèbre linéaire (DM3/2011)

Some Financial Maths Books with ISBN for Doson School

This is the list of books that we will order for the Doson School, with their ISBN numbers.

(There are too many books on the subject, and this selection is based mainly on the preferences of the lecturers).

1) B. Øksendal and A. Sulem: Applied Stochastic Control of Jump Diffusions, ISBN-10: 3540140239

2) H. . . . → Read More: Some Financial Maths Books with ISBN for Doson School

Entropy of geometric structures

Updated 06/Dec/2011: This paper is now published online in Bulletin Brazilian Math Soc, Volume 42, Number 4, 853-867:

http://www.springerlink.com/content/t623n03m400p6870/

Finally I had the courage to revise my paper on the entropy of geometric structures. The revised version is here (pdf file).

Arxiv: http://arxiv.org/abs/1109.5249

This paper is relatively simple, but I still like it very . . . → Read More: Entropy of geometric structures

Rigidity of Hamiltonian actions (revised version)

Updated 21/Oct/2011: The editors just informed us that this paper has been officially accepted for publication in Advances Math.

We have revised our paper (with Eva Miranda and Philippe Monnier) on the rigidity of Hamiltonian actions of compact semisimple Lie groups on Poisson manifolds.

The revised version is available here.

This paper was submitted . . . → Read More: Rigidity of Hamiltonian actions (revised version)

List of books to be bought for the school on financial mathematics

We want to buy some books on financial mathematics and bring them to Vietnam for the thematic school in Doson (24/Oct-01/Nov/2011).After the school, these books will be donated to a library in Hanoi.

I need  a list of  best books to buy. If you have any suggestion, please let me know by writing a . . . → Read More: List of books to be bought for the school on financial mathematics

Navier Stokes Equation in cylindrical coordinates

for incompressible flow, without external forces:

Here is the velocity field written in the cylindrical coordinate system , where is the radius and is the angle in the plane, is the pressure, and is the viscosity coefficient.

The continuity equation reads:

NB: is given by the formula , and the velocity field is:

Cylindrical . . . → Read More: Navier Stokes Equation in cylindrical coordinates