JSE
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Registered User
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Jun 12 |
awarded | ● Nice Answer |
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Jun 5 |
answered | Hyperelliptic modular curves in characteristic p |
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Jun 1 |
awarded | ● Nice Answer |
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May 22 |
comment |
Constructing Polynomial Count Varieties I agree with you that "all Frobenius eigenvalues powers of q" is a better notion than pure "polynomial point count." But I think "some power of Frobenius eigenvalue is a power of q" is better still, and takes care of examples like your (1). |
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May 13 |
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Elliptic curves over QQ with identical 13-isogeny What a nice question! I would start like this: you are looking for points on the modular surface S parametrizing pairs (E,E',C,C',phi), where E and E' are elliptic curves, C and C' are cyclic 13-subgroups, and phi is an isomorphism between C and C'. S is a quotient of X_1(13) x X_1(13) by the diagonal in the (Z/13Z)^* x (Z/13Z)^* action. Is S general type, rational, what? One could work this out and get ideas. |
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May 13 |
comment |
Show that this ratio of factorials is always an integer Now I'm curious; if {L_1, ... L_r} and {M_1, .. M_s} are linear forms in k variables, and the sum of the L_i is the same as the sum of the M_j, what further conditions guarantee that prod L_i ! / prod M_j ! is always an integer? |
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May 10 |
comment |
Modern Mathematical Achievements Accessible to Undergraduates It's Schneeberger, not Schneeberg. |
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May 10 |
answered | A Johnson-Lindenstrauss lemma for finite fields? |
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May 9 |
awarded | ● Nice Answer |
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May 9 |
answered | Concrete examples of noncongruence, arithmetic subgroups of SL(2,R) |
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May 9 |
comment |
examples of “exotic” moduli problems for elliptic curves? Yes, in some sense it explains them all! This is a result of myself and McReynolds arxiv.org/abs/0909.1851 very much inspired by the old paper of Diaz, Donagi, and Harbater, "Every curve is a Hurwitz curve." |
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May 7 |
answered | examples of “exotic” moduli problems for elliptic curves? |
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May 3 |
awarded | ● Popular Question |
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Apr 18 |
awarded | ● Favorite Question |
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Mar 19 |
comment |
The unification of Mathematics via Topos Theory Somewhat ironically, I suppose, I voted to close this because I think that, given the recent interest in the topic, it deserves a better question. For instance, I think the question BCnrd asks in comments would be a good question -- describe an example of two theories which are associated to each other in Caramello's sense, and a known theorem on one side which thereby implies ("without any creative effort," though this of course ignores Caramello's own effort!) a corresponding theorem on the other side. |
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Mar 5 |
answered | Catalan-type equations for prime powers |
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Mar 5 |
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Catalan-type equations for prime powers Actually, for 3-term arithmetic progressions, this was proved much earlier by van der Corput. |
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Mar 5 |
accepted | Which level structures on elliptic curves are twist-invariant? |
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Mar 5 |
comment |
Which level structures on elliptic curves are twist-invariant? Just considering quadratic twists! |
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Mar 5 |
awarded | ● nt.number-theory |
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Mar 4 |
answered | Which level structures on elliptic curves are twist-invariant? |
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Feb 27 |
comment |
When polynomial f(x^2) can be factored as g(x)·g(-x) ? p is a prime number, p(x) is an irreducible polynomial (named so as to emphasize that it's a prime in F_q[t].) Feel free to call them by whatever letter you like! |
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Feb 27 |
answered | When polynomial f(x^2) can be factored as g(x)·g(-x) ? |
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Feb 27 |
comment |
k3 surface as ramified double cover of $\mathbb{P}^2$ Upvoted for terseness. |
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Feb 27 |
awarded | ● Enlightened |
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Feb 26 |
accepted | Field of definition of a finite etale cover of an anabelian curve |
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Feb 26 |
awarded | ● Nice Answer |
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Feb 26 |
accepted | Elliptic curves over QQ with isomorphic n-torsion |
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Feb 25 |
answered | Field of definition of a finite etale cover of an anabelian curve |
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Feb 25 |
answered | Elliptic curves over QQ with isomorphic n-torsion |
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Jan 23 |
comment |
Can the n-string sphere braid group embed in to the (n+1)-string sphere braid group? Any such sequence of embeddings would certainly have to be very funny-looking, and in particular would lack some of the properties that makes the braid group story so appealing. For instance: the H_1 of the spherical braid group on n strands is (Z/2nZ) (or something like that) and so your maps, maybe apart from some order-2 business, are going to have to send each spherical braid group to the commutator of the next, just because (Z/2nz) doesn't map so well into (Z/2(n+1)Z). |
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Jan 6 |
accepted | What is a random number? (poll experiment) |
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Jan 5 |
comment |
Can every curve be written as $f(x)=g(y)$? I'm totally going to start saying "Harris and Mumford proved that the generic genus g curve is not Zieve." |
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Jan 5 |
awarded | ● Nice Answer |
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Jan 5 |
revised |
What is a random number? (poll experiment) added 717 characters in body |
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Jan 4 |
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New grand projects in contemporary math But e.g. the paper of Candes and Recht that just won the Lagrange Prize places compressed sensing within a bigger and more conceptual theoretical framework. That's what I mean by pushing back on "compressed sensing" as a name for the whole field. By the way, thanks to YF for linking to my Wired piece -- but for anybody reading MathOverflow, Terry's blog post is going to offer you much more than my magazine article, which is very simplified! |
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Jan 4 |
awarded | ● Good Answer |
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Jan 2 |
revised |
New grand projects in contemporary math edited body |
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Jan 2 |
awarded | ● Nice Answer |
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Jan 2 |
accepted | Algorithm for determining whether two polynomials have the same splitting field |
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Jan 2 |
revised |
New grand projects in contemporary math added 22 characters in body |
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Jan 2 |
answered | New grand projects in contemporary math |
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Jan 2 |
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New grand projects in contemporary math And yes, it counts as math! |
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Jan 2 |
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New grand projects in contemporary math where the stabilizer is a form of SO_3 -- but now the group law is coming from the map H^1(K,SO_3) -> H^2(K,+-1) and there is a cohomological explanation in kreck's other sense. As far as I know, "every composition law is a cohomological law" among those observed so far. |
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Jan 2 |
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New grand projects in contemporary math (Forgive me if any of this is wrong, I'm rushing.) For binary cubic forms, you have a composition law only among those pairs with the same quadratic resolvent; the law is actually coming cohomologically from the SL_2 action, whose stabilizer is a form of Z/3Z whose H^1 reads off (more or less) the 3-torsion in the class group of an appropriate quadratic ring. So this one fits kreck's formulation. The only one I know which doesn't is the case studied by Gross and Lucianovic (continued next comment) |
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Jan 2 |
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New grand projects in contemporary math I would say that the grand project is better described as "sparse inference," where we try to reconstruct data that is known or expected to be sparse in some basis (or low-rank, or in some other way restricted to a low-dimensional but badly nonconvex subspace of parameter space.) This includes compressed sensing but also a much bigger circle of ideas (L^1 minimization, convex relaxation more generally, hierarchical clustering, manifold learning, etc.) I have learned a ton from talking to people about this stuff and I hope more pure mathematicians will get in on it! |
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Jan 2 |
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Algorithm for determining whether two polynomials have the same splitting field Depends what the bounds in Lagarias-Odlyzko are and I don't have them in my head right now. You might look at a recent paper of Kowalski and Zywina which carries out a computation of this kind in real life. |
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Jan 2 |
answered | What is a random number? (poll experiment) |
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Jan 1 |
answered | Algorithm for determining whether two polynomials have the same splitting field |
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Dec 29 |
answered | finite abelian p-groups with solvable automorphism group |
