19,581 reputation
354135
bio website umpa.ens-lyon.fr/~serre
location Lyon, FRANCE
age 60
visits member for 4 years, 10 months
seen 7 mins ago

My research activity is mainly in PDEs, with applications to Physics, especially in Fluid Dynamics. I have written a 2-volume book on Conservation laws, and a book about the Hyperbolic IBVP (in collaboration with S. Benzoni-Gavage). I have edited in collaboration with S. Friedlander, a 4-volume 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 $(n-1)^2$-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