A liberally educated person meets new ideas with curiosity and fascination. An illiberally educated person meets new ideas with fear
by James B. Stockdale

Eight Vietnamese win Hellman/Hammett Human Rights Award

Source: Human Rights Watch

(Bangkok) – Eight Vietnamese writers are among a diverse group of 48 writers from 24 countries who have received the prestigious Hellman/Hammett award recognizing writers who demonstrate courage and conviction in the face of political persecution, Human Rights Watch said today [14/Sep/2011]

“Vietnamese writers are frequently threatened, assaulted, or even . . . → Read More: Eight Vietnamese win Hellman/Hammett Human Rights Award

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

Lectures on Poisson Geometry (Geometry and Topology Monographs, Vol. 17)

Finally, “Lectures on Poisson Geometry”, which is a collection of lectures on various aspects of Poisson geometry, edited by T. Ratiu, A. Weinstein, and myself, has appeared as Volume 17 of the series Geometry and Topology Monographs:

http://pjm.math.berkeley.edu/gtm/2011/17/

Poisson geometry is a rapidly growing subject, with many interactions and applications in areas of mathematics . . . → Read More: Lectures on Poisson Geometry (Geometry and Topology Monographs, Vol. 17)

Nondegenerate singularities of integrable non-Hamiltonian systems

Last updated: 07/Apr/2011

The purpose of this note is to study nondegenerate singularities of integrable non-Hamiltonian systems. In particular we want to extend the Vey-Eliasson theorem about the local linearization of nondegenerate singularities of integrable Hamiltonian systems to the non-Hamiltonian case, and show that, in the non-Hamiltonian case, nondegenerate singularities are also rigid and . . . → Read More: Nondegenerate singularities of integrable non-Hamiltonian systems

Topology of integrable non-Hamiltonian systems

Last updated: 01/Apr/2011

This is a research project on which a PhD student of mine is working with me. Please don’t steal the ideas and results that I discuss here.

The problem is to study the topology and geometry of proper non-Hamiltonian integrable dynamical systems on manifold. A non-Hamiltonian integrable system consists of:

* . . . → Read More: Topology of integrable non-Hamiltonian systems

Hidden symmetries of mathematical objects

A general philosophy is that, mathematical objects have symmetry groups, and can be classified by these groups. The Galois theory is an example. Transformation groups or groupoids, linear representation theory, classification of metrics by holonomy groups, etc.,  are also instances of this philosophy.

There are objects, which a-priori have no symmetries, but still have . . . → Read More: Hidden symmetries of mathematical objects

Solar Power Industry Analysis

(This is a report that I made for a seminar on financial mathematics and investing, and a small investment fund created by the participants of this seminar. This report is not a recommendation to buy or sell anything to anyone else).

Key findings:

* Solar energy is the best source of energy: abundant, free, . . . → Read More: Solar Power Industry Analysis

Rigidity of Hamiltonian actions

Finally (after several years of dragging our feet), my colleagues Eva Miranda and Philippe Monnier and I have just finished our paper on the rigidity of Hamiltonian actions of compact semisimple Lie groups on Poisson manifolds.

The rigidity phenomenon here is quite natural. It has been  known for a long time that compact group . . . → Read More: Rigidity of Hamiltonian actions

Notes on INS (14): CKN theory

Last updated: 27/Oct/2010

CKN stands for Caffarelli-Kohn-Nirenberg. The theory is about partial regularity of solutions of INS. One should probably add the name of Scheffer, who introduced the concepts that CKN improved/generalized.

The main result is that the (parabolic) 1-dimensional Hausdorff measure of the (hypothetical) singular set in space-time is zero (which means that, . . . → Read More: Notes on INS (14): CKN theory

Topology and stability of integrable Hamiltonian systems

There is a new survey paper by A. Bolsinov, A. Borisov and I. Mamaev about the topology and stability of integrable Hamiltonian systems in Russian Mathematical Surveys (Vol. 65, 2010, No. 2, pp  259–318). A copy of it can be downloaded here. In this paper, the authors discuss the topology of (finite dimensional) integrable . . . → Read More: Topology and stability of integrable Hamiltonian systems

Notes on INS (4): Useful inequalities & spaces

Last updated: 25/Oct/2010

There are two many inequalities used in the theory of Navier-Stokes equations. I’ll have to keep track of them. So this is the place where I put the inequalities.

Gagliardo-Nirenberg-Sobolev  (GNS). Assume . Then there exists a positive constant , depending only on and , such that for all (space of . . . → Read More: Notes on INS (4): Useful inequalities & spaces

Notes on INS (3): Koch-Tataru theorem (small initial data)

Last updated: 16/Oct/2010

Existence of smooth global solutions for small initial conditions

The strongest (and in a sense optimal ?) result in this direction is due to Koch and Tataru (2001).

Reference: H. Koch, D. Tataru, Well-posedness for the Navier-Stokes equation, Adv. Math. 157 (2001), No. 1, 22–35.

See also: P. Germain, N. Pavlovic, . . . → Read More: Notes on INS (3): Koch-Tataru theorem (small initial data)

Notes on INS (2): non-existence of self-similar solutions

Non-existence of self-similar solutions

Last updated: 13/Oct/2010

See the first part here: Notes on INS (1)

In this part, we will look at the proof of the non-existence of self-similar singular solutions to the INS equation.

The main reference is: Neças, Ruczicka and Sverak (Acta Math., Vol 196, 1996)

We will first follow the . . . → Read More: Notes on INS (2): non-existence of self-similar solutions