7,860 reputation
12752
bio website perso-math.univ-mlv.fr/users/…
location Paris, France
age 34
visits member for 5 years, 1 month
seen 17 hours ago

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


1d
comment Distance Between two points
You should sure know the formula for finding it. Why don't you learn it? If this is your homework, the formula is certainly in your book or notes. In any case, your question is inappropriate here.
2d
comment Singularities in minimal surfaces
Your question is unclear: are you talking about minimal surfaces (which are smooth, as you say) or soap films? In the later case, there are several possible definitions, but my understanding of Jean Taylor's work is precisely that the minimal cones she classified are the infinitesimal models for soap films. Either way, it looks like you answered your own question, but I may have overlooked something.
Apr
22
awarded  Good Answer
Apr
22
comment A measure on the space of probability measures
However there is little hope to derive an equivalent to Hausdorff measure: for similar spaces, namely the set of closed subsets of the interval, it has been shown that any analogue of a Hausdorff measure is either zero or not $\sigma$-finite (see references in the above-mentioned papers).
Apr
22
comment A measure on the space of probability measures
Whenever $X$ is infinite, the Hausdorff dimension of its Wasserstein space is infinite. One can still define related invariants and compute them: I did precisely that in perso-math.univ-mlv.fr/users/kloeckner.benoit/papiers/… then improved in perso-math.univ-mlv.fr/users/kloeckner.benoit/papiers/…
Apr
22
comment A measure on the space of probability measures
@SimonHenry: in many cases, there are measures on $X$ that one can take as reference (e.g. Riemannian volume on a compact manifold, Lebesgue measure on $[0,1]$, etc.); also it makes more sense to study $\mathcal{P}(X)$ as a metric measure space as is asked here when $X$ itself is a metric measure space, in which case one does have by definition a reference proba on $X$.
Apr
12
answered Your favorite surprising connections in Mathematics
Apr
12
comment Your favorite surprising connections in Mathematics
@Vectornaut: your point is that this connection can be understood; but it still strikes me as initially surprising.
Apr
12
comment Your favorite surprising connections in Mathematics
Well, last time I had to teach that and tried to remember how it is proved, I realized that in fact that is the definition of $\pi$ (as soon as one parametrizes the unit circle by $e^{it}$ and sees that this curve has constant speed one, that is).
Apr
11
accepted Classification of ergodic measures for circle expanding maps
Apr
11
awarded  Enlightened
Apr
11
awarded  Nice Answer
Apr
11
revised Can any simplex shadow-project to a regular simplex?
Corrected the mistake pointed out by Will Sawin
Apr
11
comment Can any simplex shadow-project to a regular simplex?
Oh right! I performed a product of degrees of freedom instead of a sum. That's kind of embarrassing, but at least it will give some indulgence next time a student uses the first operation he can think of to answer a question.
Apr
11
comment Most interesting mathematics mistake?
I must add to this that this story is even linked with modern developments, in the following direction: if the 5 conics are all real, how many among the 3264 conics tangents to all 5 of them are real? In 1997, Ronga, Tognoli and Vust found an example where all 3264 tangents conics are real. In 2005, Welschinger proved that if the 5 conics are ellipses, no two nested one inside the other, then at least 32 of the 3264 tangent conics must be real. This is related to a lot of deep modern tools.
Apr
11
answered Can any simplex shadow-project to a regular simplex?
Apr
10
comment Notation for $\log \log \cdots \log n$?
There is room for confusion for the $n$th derivative of the $\log$ function, though.
Apr
6
answered Terminology for metrics?
Apr
4
awarded  Nice Answer
Apr
3
comment Natural probability on integers
I guess that by using even more barely convergent series like $\sum n^{-1}(\log n)^{-s}$ or $\sum n^{-1}(\log n)^{-1}(\log\log n)^{-s}$, you can get smaller remainders...