206 reputation
17
bio website
location
age
visits member for 2 years, 5 months
seen yesterday

Aug
27
comment Why study Algebraic Geometry?
Dear Javier, it's "Stanford" not "Standford" (re: Ravi's notes).
May
19
awarded  Yearling
Dec
2
comment Tensors constructed out of metric other than the Riemann curvature tensor
I am pretty surprised to hear this. Do you know off the top of your head if the same thing is true for Lorentzian manifolds and manifolds with other signatures? (If not don't worry, I can work through the proof you cited if need be.)
Jul
31
awarded  Citizen Patrol
Jul
31
comment On analytic functions $f,g$ with the sum of their norms is constant
This has appeared a few times: math.stackexchange.com/questions/96257/… and math.stackexchange.com/questions/81030/…. The statements are not word-for-word the same as yours, but the accepted proofs go through basically verbatim for your problem.
Jul
27
comment Probability of a winning consecutive $k$-subset out of $n$ coin flips
Thanks for this! It's nice to see how slow the growth is in practice. In fact by using principles from the theory of large deviations you can see that, almost surely, the largest admissible $k$ is $\gg \log n$. By this I mean that if $C_n$ is the random variable denoting the length of the longest consecutive "> 50% winning" subsequence in $n$ tosses, then $\lim_n C_n/\log n = \infty$ almost surely.
Jul
5
comment Writing Integrals using Differential Forms
If you haven't seen this before then think about this: $dx$, $dy$, and $dz$ aren't special to your curve/surface/whatever, they come out of your ambient space. Sometimes it's nice not to have to assume anything about an ambient space and thus define and work with forms intrinsic to the manifold. I hope this makes sense, at least on some superficial level.
Jul
5
comment Writing Integrals using Differential Forms
Careful, in the wiki article $n$ is the dimension of the manifold (and not the ambient space). So indeed $n = 1$ and $n = 2$ in your two examples. Your confusion isn't unwarranted- there is a subtlety here. Very loosely speaking, in your entire post you've been working with differential forms of the ambient space ($dx$, $dy$, $dz$), whereas in slightly more "advanced" treatments of Riemannian geometry (such as the one in the wiki article) they work with differential forms of the manifold. It's a good exercise for you to figure out how one transforms into the other.
Jul
5
comment Writing Integrals using Differential Forms
Vincent, what you're looking for is the volume form: en.wikipedia.org/wiki/Volume_form
Jun
26
awarded  Commentator
Mar
12
comment Martingale inequality related to Kolmogorov's maximal inequality
It looks like your question got overlooked. Somebody else asked the same question a couple of weeks ago. You can find my answer over there: math.stackexchange.com/questions/313415/…
Mar
5
awarded  Critic
Mar
4
awarded  Informed
Mar
2
revised Martingale and bounded stopping time
added 2 characters in body
Mar
2
answered Martingale and bounded stopping time
Jan
7
comment Is the area of intersection of convex polygons always convex?
You are welcome my friend.
Jan
3
revised Is the area of intersection of convex polygons always convex?
describe algorithm to find maximal triangle + improved formatting
Jan
3
comment Is the area of intersection of convex polygons always convex?
Thanks Sigur! Now I see what was going on with Rahul, I guess the OP also wanted a way to determine what the maximal triangle is. My apologies for missing that. You're right Sigur, I think maximizing among all pairs $(L, h_L)$ is the best way to do it, let me edit my post above to reflect your point.
Jan
3
comment Is the area of intersection of convex polygons always convex?
This isn't getting us anywhere :-) If perhaps you think my original presentation is not clear, I will be happy to throw in more details to straighten it out.
Jan
3
comment Is the area of intersection of convex polygons always convex?
Hi Rahul, I'm afraid I don't understand the point you're making. EDIT: To be clear, as you pointed out, this was not supposed to be a constructive method for global maxima (i.e. start with a triangle, wiggle it around, construct a global maximum). All it does is start with a triangle and make a triangle that is at least as good, and whose vertices are nice. So bootstrap it with a maximal triangle and voila.