bio  website  umpa.enslyon.fr/~serre 

location  Lyon, FRANCE  
age  60  
visits  member for  4 years, 10 months 
seen  7 mins ago  
stats  profile views  11,517 
My research activity is mainly in PDEs, with applications to Physics, especially in Fluid Dynamics. I have written a 2volume book on Conservation laws, and a book about the Hyperbolic IBVP (in collaboration with S. BenzoniGavage). I have edited in collaboration with S. Friedlander, a 4volume Handbook of Mathematical Fluid Dynamics.
I have a continuous interest in Matrix Analysis. I have written a Graduate Text about Matrices. The second edition has been released in November 2010.
23h

answered  Determinant of block tridiagonal matrices 
1d

revised 
Maximum of the Vandermonde determinant / minimum of the logarithmic energy
added 1 character in body 
1d

comment 
Maximum of the Vandermonde determinant / minimum of the logarithmic energy
Yes, I have to edit my post ! 
2d

answered  Maximum of the Vandermonde determinant / minimum of the logarithmic energy 
Jun 27 
comment 
A curious determinantal inequality
I tried with the choice $A^{1/2}={\rm diag}(2,1)$ and $B^{1/2}=\begin{pmatrix} 1 & 1 \\ 1 & 2 \end{pmatrix}$, which fails to pass the test $D^2+E^2=1$. 
Jun 27 
comment 
A curious determinantal inequality
I doubt too that $D^2+E^2$ equals $1$. 14 votes pro without a verification ? 
Jun 17 
awarded  Good Answer 
Jun 12 
answered  How much redundancy resides in an $n \times n$ orthogonal matrix? 
Jun 9 
comment 
Is there a big solvable subgroup in every finite group?
This definition might not be universally accepted. I have once learned that a proper subgroup $H$ of $G$ is big if it intersects every conjugacy class. For instance the triangular subgroup is big in ${\bf GL}_n(\mathbb C)$. In a finite group, there does not exist such a big subgroup. 
Jun 9 
comment 
When is the convex hull of two space curves the union of lines?
You could as well consider the convex hull one one curve. This amounts to chosing $B=A$. 
Jun 8 
awarded  Popular Question 
Jun 5 
comment 
Why is there a connection between enumerative geometry and nonlinear waves?
Don't think about KdV as a fluid equation. It is just a normal form in the realm of nonlinear dispersive PDEs. You encounter it at every intersection. 
Jun 4 
comment 
which norms can be realized as operator norms?
Yes indeed. It is a general fact that operator norms have rather flat unit sphere. For instance, the norm on ${\bf M}_n(\mathbb R)$ induced by $\ell_p$ is constant over the $(n1)^2$dimensional convex set of bistochastic matrices ! 
Jun 4 
revised 
which norms can be realized as operator norms?
edited body 
Jun 4 
answered  which norms can be realized as operator norms? 
Jun 4 
revised 
which norms can be realized as operator norms?
added 16 characters in body 
Jun 4 
comment 
The unpublished papers in reference to the published papers
@Willie. Quid got it. As you can see, Google Schollar list 360 citations of this paper ! It was a seminal paper in weak KAM theory, as well as in homogenization theory. 
Jun 4 
answered  The unpublished papers in reference to the published papers 
Jun 3 
comment 
Derivatives of radial functions can be bounded by derivatives in terms of radial distance?
@Terry. Nice contribution. I'll think about it. By the way, I remember your definitive answer to my question mathoverflow.net/q/51848/8799 . 
Jun 3 
revised 
Derivatives of radial functions can be bounded by derivatives in terms of radial distance?
added 8 characters in body 