bio | website | perso.ens-lyon.fr/… |
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location | Lyon, France | |
age | 37 | |
visits | member for | 4 years, 4 months |
seen | 4 hours ago | |
stats | profile views | 2,909 |
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 |