My solution plan was too ambitious, I'm afraid. I tried to work out the details and I found it way more challenging then I expected. I still think that there...
The short answer is: yes. The geometry of the situation seems to be this. We have the orthogonal group O(3), which comes in two pieces: the rotations SO(3),...
It seems we don't have to work too hard to understand the regulii in O(3). First, unless I am confused it should be enough to understand the regulii of S^3...
I've been batting my head against the problem of trying to control the very rich rotations (k >> n^{2/3}) and not getting very far. But one thing which...
Another brief remark on regulii: if we select three skew circles in S^3, then the collection of all circles that intersect each of these three circles forms a...
Dear all, I would like to post on my blog on the geometric interpretation of the Elekes-Sharir-Guth-Katz miracle that "lines" l_{AB} in SE(2) become genuine...
First of all, I approve the blog posting. I think in any rate we have gone so much of the way towards 3D (and higher) Erdos that we are unlikely to be scooped...
I'm sure that everything that can be done for S^2 can also be done for H^2 - the algebraic structures are almost identical (they are Wick rotations of each...
I too have no problem with the blog posting. I uploaded the file "Explicit Line L_{a->b}.pdf" to the yahoo group, which describes an explicit parametrization...
I think the blog post is a good idea, I'm looking forward to read it! I was wondering if there is an easy explanation why the analogous argument fails on the...
Yes, Alex showed me this paper yesterday. It is close to what I discussed on the blog; whereas the Erdos distance problem is set in Euclidean space SE(2) /...
Indeed, this is in the original e-mail I sent... (see last sentence) "Then the general "Erdos distance problem" -- which we might call in this case an "Erdos...
... Well, in this case, there is a sleazy way out: the SL_2(R)/R theory tells us that given N points (not all collinear), there are > N/log N areas of ...
Dear All, I don't want to interrupt the line of our proof for higher dimensional distinct distances, but let me mention another way to see the distance problem...
Hmm, this is a nice formulation, though it seems to me that it would bound not only the distinct distances, but the pinned distances (the number of distances...
That pinned-distance problem is nice, actually! You could even ask for something a priori slightly stronger; that there are no more than N^2 isosceles...
I believe the problem of too many lines lying on a regulus can be dealt with without too much difficulty if we are free to choose which point is our "origin."...
excited to read josh's latest, am full of percocet right now post-elbow-surgery so it may be a couple of days just a note: another 3-dimensional group acting...
Oops; I believe my previous email dealing with regulii dealt with an old formulation of the problem in which we only had to deal with great circles in SO(3)...
Josh, can you unpack the statement below for me? I'm confused by it -- I thought we had it in mind that the incidence geometry of 1-dimensional guys in...
I made a mistake in my dimension counting---every line (or at least a Zariski open subset of them) can arise as a line of the form L_{a->b}, so please...
OK, cool. I do think that in dimensions higher than 3 it will start being the case that the set of point-pairs joines by a "line" has higher and higher...
hi guys one thought in a different direction, recorded briefly. i was wondering whether we could perhaps get mileage from an "approximate" version of guth-katz...
Jordan: Read this: http://nyjm.albany.edu/j/2001/7-10.pdf Take special note of the example illustrated on page 151. However, if you are in a position to get...
I think I'm still confused about where the cone comes from. I take it Josh is working in the a copy of O(3) fixing some chosen point O. But then it seems to...
got dimension count wrong, i think i understand better what josh was saying now, more later...
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erdos@yahoogroups.com
Mar 31, 2011 5:04 pm
Hello, This email message is a notification to let you know that a file has been uploaded to the Files area of the erdos group. File : /3d erdos.pdf ...
