4,784 reputation
11734
bio website perso.ens-lyon.fr/…
location Lyon, France
age 37
visits member for 4 years, 4 months
seen 4 hours ago
I am a number theorist working in Lyon (France).

Oct
5
answered Representation of vectors in $\mathbb{R}^2$ via differences of small vectors.
Sep
21
comment problems of subspace of M_n(C)
It's probably easier if the field is $\mathbb{C}$. For example take $k=n$ so the question is about subspaces such that any nonzero matrix is invertible. You see that any $2$-diml space of matrices contains noninvertible matrices (because if $A,B$ are two invertible matrices, then $\det(A+X \cdot B)$ has roots in $\mathbb{C}$). However, the corresponding problem over $\mathbb{R}$ is much harder, and is related to the maximal number of linearly independent vector fields on a sphere, which involves $K$-theory. See en.wikipedia.org/wiki/Vector_fields_on_spheres for details.
Aug
31
answered Numerical evidence of Beilinson's conjecture in local fields and function fields
Aug
25
awarded  Nice Answer
Aug
25
awarded  Editor
Aug
25
revised Refereeing a Paper
deleted 23 characters in body
Aug
25
answered Refereeing a Paper
Aug
23
awarded  Enthusiast
Aug
11
answered Power series $f$ such that $f(\zeta_{p^n}-1)=1/p^n$ for almost all $n \geq 0$
Jul
7
comment Subspaces of finite codimension in Banach spaces
Here's a fun exercise: take $E$ to be a Banach space and let $H$ be a codimension one subspace. Prove that $H$ is dense in $E$ if and only if $E \setminus H$ is arcwise connected.
Jul
5
answered Extension of valuation
Jun
23
awarded  Necromancer
Jun
11
comment Knuth's intuition that Goldbach might be unprovable
We do know that every even number is the sum of a prime and either a prime or a product of two primes. This makes the existence of a proof of Goldbach's conjecture sound rather plausible to me.
May
26
awarded  Enlightened
May
26
awarded  Nice Answer
May
25
comment Naive questions about “matrices” representing endomorphisms of Hilbert spaces.
It's chapter five in the 2nd edition, but there's still no counterexample...
May
25
answered Naive questions about “matrices” representing endomorphisms of Hilbert spaces.
May
2
awarded  Autobiographer
May
2
comment If the tensor product of two representations are crystalline, are the original representations crystalline?
I asked my student to do this in December of 2009. As far as I can remember, it was Barry Mazur who asked me this question when I was at Harvard (so that was at least 5 or 6 years ago). If I remember correctly, he wanted to know what "Sym^2 V crystalline" implied about V. Between then and now, a couple more people asked me the more general question about V \otimes W (I unfortunately don't remember their names). In both cases, I told them the method which I thought would solve the problem, and didn't hear back from them.
May
1
awarded  Enlightened