If the teacher be corrupt, the world will be corrupt.
by Persian proverb

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

Notes on INS (1): in the beginning …

Last updated: 30/Oct/2010

INS = incompressible Navier-Stokes equation:

, where and

These are the notes that I’ll write about this problem, in order to learn about it and keep track of it.

Unless otherwise indicated explicitly, the domain will be , no external field, the initial condition (velocity field) will be smooth and . . . → Read More: Notes on INS (1): in the beginning …

Modeling complex systems by macroscopic models (lecture by Pierre Degond, 03/09/2010)

Complex means multi-agent

Often no leader, only local interactions, but exhibits large scale structures (self-organization, emergence)

Continue reading Modeling complex systems by macroscopic models (lecture by Pierre Degond, 03/09/2010)

Lichnérowicz prize in Poisson geometry

I will not have much time to work on Poisson geometry any more, but since this is a field to which I was attached during many years, I feel compelled to write about it here.

Since 2008 there is a new prize in mathematics, called the “Lichnérowicz prize”, in the field of Poisson geometry. . . . → Read More: Lichnérowicz prize in Poisson geometry

My talks at IMPA (streaming videos)

Geometry of Gelfand-Cetlin integrable system (Conservative dynamics and symplectic geometry  2009):


Dynamics on Poisson manifolds (Poisson 2010):


(now that I listened to my own talk at IMPA, I found that my English was really horrible !)

For all video lectures recorded by IMPA:


How to destroy universities ?

Tired of doing theoretical research, I’m now learning about how to build good universities. It turns out that to build good universities is really difficult, you need a lot of good conditions, and decades or even centuries. But to destroy universities (literally or figuratively) is much easier, and there are policies and actions with “good intention” (aiming to improve universities) which actually destroy universities. (As they say, the road to hell is paved with good samaritans). So even if you don’t want to destroy universities and instead want to build universities, you should also know about those “good-sounding” policies which destroy universities in order to avoid them.

I’m collecting here the “most effective methods” to destroy universities. If you know of other methods, please send them to me. Thank you !

Continue reading How to destroy universities ?

Lecture Notes of Summer School on Financial Maths

The lecture notes + computer files of the Summer School on Mathematical Methods in Finance and Economy 2010 can be found here:


Materials for the course on portfolio management can be found here:


The rise and fall of commureligion

What is commureligion?

It’s a dictatorship of a religion, which promises heaven (paradise) for the poor people.

It was created some 2 thousands years ago (there are people who say only 1 thousand years) by a gang of religious revolutionaries, headed by a guy called Zecu.

Zecu was not very happy that the god-rich . . . → Read More: The rise and fall of commureligion

Hans Duistermaat passed away

I just heard from a colleague that Hans Duistermaar passed away yesterday (March 18th). To me, Hans was not only a great mathematician, but also a great friend. This sad news came as a shock for me.

Hans made many important contributions to mathematics: Fourier integral operators (with Hormander), symplectic geometry (equivariant cohomology and . . . → Read More: Hans Duistermaat passed away

What Can You Gain From A Mathematics Degree?

Mathematical skills, of course, why ask ?

Actually, according to this webpage of the Math Department, University of Warwick, you can gain not only math skills, but also a lot of other essential  skills too:

Mathematical Skills. As a mathematics student you will study each of the major subject areas of modern mathematics: algebra, . . . → Read More: What Can You Gain From A Mathematics Degree?

It’s official: mathematics is the best profession

An interesting articlein WSJ about mathematics as the best profession in the US:


Ranking (by the level of satisfaction) of 200 different professions:


Thanks to Huong for letting me know about the WSJ article