7,598 reputation
12548
bio website perso-math.univ-mlv.fr/users/…
location Paris, France
age 34
visits member for 5 years
seen 2 hours ago

I am a teacher and researcher at Université Paris-Est Créteil.


14h
comment Does a (non-closed) differential 1-form define a curve?
But then I don't see what you mean by the integral of a function along a curve; and whatever that means, it is pretty clear that such a $C$ would not be unique. I maintain my vote to close.
14h
comment Does a (non-closed) differential 1-form define a curve?
Your question does not make much sense: what is $V$ in the integrals? What is $S$? How would you expect to define a curve by such an integral?
16h
awarded  Yearling
18h
asked Geometry of rings and semi-rings
1d
comment Concise disambiguation of Voronoi boundaries
These method has the inconvenient of breaking the symmetry of the numbering though; you can decide to break ties by choosing the $i$ such that $x_i$ has least first coordinate, then the least second coordinates. This might be what you meant by lexicographic ordering, but it should be no trouble to define $i(x)$ as above with the current tie breaker.
1d
comment Concise disambiguation of Voronoi boundaries
I don't see the problem with the ordering idea. Either define $V_i$ by induction, adding the assumption that $x\notin V_j$ for all $j<i$ in the definition of $V_i$ ; or define $i(x)$ as the $i$ in $\{1,\dots,n\}$ such that $|| x-x_i ||\le || x-x_j ||$ for all $j$, and let $V_i=\{x : i(x)=i\}$.
1d
comment Are normal deformations of an embedding open in the $C^{\infty}$-space of embeddings of a compact smooth manifold`
Maybe with less formalism, one can use the nearest neighbor projection $\pi : T\to j(M)$, well-defined from a tubular neighborhood $T$ of $j(M)$. Let $\ell$ be any embedding of $M$ which is $C^1$ close to $j$: then $\ell(M)\subset T$, and by the inverse function theorem $\pi\circ \ell$ is an embedding; since it has the same image as $j$, it differs from it by a diffeomorphism and you are done.
Mar
18
comment 'Unitary' charts on odd-dimensional spheres
Just as Robert Bryant, I am puzzled by your assertion that $\mathbb{C}^n\times \mathbb{R}$ be CR-isomorphic to any open set of the sphere: to phrase Robert's objection differently, they live in opposite parts of the CR world, the former being Levy-flat and the later being strictly pseudoconvex. The relevant keyword is probably "Heisenberg group": in one of its guises, it is a pseudo-Riemannian manifold that parametrizes any complement of a point in the unit sphere of $\mathbb{C}^n$, and it can certainly be endowed with a natural CR-structure.
Mar
16
answered Maximum degree and matching number
Mar
12
comment Closed geodesics that cross one another frequently
It seems that another example could be constructed by simply adding $n$ spikes along an equator of the sphere; the two curves that zigzag between the pikes and locally minimize length would have the required intersection.
Mar
11
answered Lie group action on a finite dimensional flat manifold
Mar
7
comment The probability that a 2d continuous time random walk avoids the origin
A brownian motion has probability $0$ to return to exactly $0$. It will return arbitrarily close to $0$ arbitrarily often, but you have to add an allowable distance to $0$ in the mix to phrase your problem correctly.
Mar
6
reviewed Approve Dihedral extension of 2-adic number field
Feb
28
comment Classification of ergodic measures for circle expanding maps
I was aware of the relation with the shift, but wanted to stress Furstenberg's conjecture (which cannot be stated for shifts as they act on different spaces). Universality I didn't know, this sure shows how hopeless it is to imagine a precise classification; but maybe there is something to be hoped when using the metric on the circle; for example maybe one could say something about not-too concentrated measures (e.g. $\mu([a,b])\le C|b-a|^\alpha$ for some $C$ and $\alpha<1$).
Feb
28
asked Classification of ergodic measures for circle expanding maps
Feb
28
reviewed Approve How to determine the homotopy groups of the suspension of a space?
Feb
28
reviewed Approve How to determine the homotopy groups of the suspension of a space?
Feb
28
reviewed Approve How to determine the homotopy groups of the suspension of a space?
Feb
27
comment Do you know of any asymmetric, nonparametric measure of dependence?
I took the liberty to include the description, slightly edited, to your answer (this is more practical for other readers). Could you please precise which other axioms your measure satisfies? E.g. is the dependency zero if and only if $X$ and $Y$ are independent? Don't you get any kind of invariance under change of parameter on the $Y$ side?
Feb
27
revised Do you know of any asymmetric, nonparametric measure of dependence?
Added the description of the paper from the author's comment