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Mathematics professor at Cambridge
Jun 18 |
comment |
Are there very strongly pseudorandom permutations?
I have now found a source that seems to suggest that the Luby-Rackoff construction won't give hardness greater than $2^n$. So it looks as though a different idea would be needed. But maybe there are some different ideas out there. |
Jun 18 |
asked | Are there very strongly pseudorandom permutations? |
Jun 13 |
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Are there any very hard unknots?
I drew the "quotient" knot and the picture has been sitting on my desk for about a month. At first it looked hard to simplify, but then I saw that one could make a "hole" in the middle and take a chunk of knot and pass it up through the hole and back down again. This kind of global untwisting would, I think, have to be part of any unknotting procedure of the kind I fantasize about. At some point I might make the knot out of string and see whether I can indeed untie it fairly straightforwardly starting with that move. |
Jun 12 |
awarded | Nice Answer |
Jun 6 |
awarded | Favorite Question |
May 24 |
awarded | Popular Question |
May 9 |
comment |
Are there any very hard unknots?
Thank you for this example. It's quite interesting as it is in some sense a "product" of smaller knots. I tried replacing the bundles of strands (most of the time four strands) by a single strand and obtained a picture of a knot that I can't instantly see to be the unknot, though I did find a local way of reducing the number of crossings. If this "quotient" knot is not the unknot, then it's a very interesting example. |
Mar 30 |
awarded | Good Answer |
Mar 29 |
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What can be proved about the Ramanujan conjecture using elementary means?
I don't mind complex analysis, but I'm wondering whether a "non-structural" proof is possible. Without saying precisely what I mean by that, I would say that modular forms are on the wrong side of the boundary. |
Mar 29 |
revised |
What can be proved about the Ramanujan conjecture using elementary means?
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Mar 29 |
revised |
What can be proved about the Ramanujan conjecture using elementary means?
added 619 characters in body |
Mar 29 |
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What can be proved about the Ramanujan conjecture using elementary means?
Ah, I see the point now. OK, I'll go back and add a condition. |
Mar 29 |
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What can be proved about the Ramanujan conjecture using elementary means?
I'm taking $1-q^{a_r}$, and not $1+(-q)^{a_r}$. |
Mar 29 |
awarded | Nice Question |
Mar 29 |
asked | What can be proved about the Ramanujan conjecture using elementary means? |
Mar 2 |
awarded | Popular Question |
Mar 2 |
awarded | Good Question |
Feb 7 |
awarded | Good Answer |
Nov 28 |
awarded | Nice Answer |
Nov 22 |
awarded | Nice Answer |