S. Carnahan
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Moderator ♦
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I think this is a neat project.
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2h |
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Examples of interesting false proofs I think it is more likely that at least 12 voters don't see puns as examples of interesting false proofs. In the event that you feel the absolute need to publicly communicate your displeasure, could you please find a way that doesn't involve insults? |
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4h |
answered | Is there a topograph for Pythagorean triples? |
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4h |
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Is there a convenient differential calculus for cojets? @Ricardo: Yes, you're correct that if you have a global trivialization of your vector bundle (i.e., taking jets with values in a vector space), you get an additive structure. However, without a fixed trivialization, you don't get linear maps on jets of order greater than one. For example, the transition between the north-pole and south-pole stereographic projections on $S^1$ produces a quadratic term on tangent 2-jet coordinates: if $z = 1/w$, then $d^2z = -\frac{2}{w^3} (dw)^2 - \frac{1}{w^2}d^2w$. |
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14h |
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And old hat with a new plume How well does this reasoning work when there are only one or two islanders? |
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17h |
awarded | ● Nice Answer |
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1d |
answered | The proportion between permutations and derangements. |
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1d |
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Is there a scheme corresponding to the unit interval? Since non-empty schemes have lots of geometric points, there is some set-theoretic subtlety in defining $I$. One can always restrict inputs to low levels of $V$ to get a more digestable but slightly less universal object. |
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1d |
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Functions about integers which are divisible by all numbers less than or equal to a fractional power of the integer What do you want to do with this function, aside from defining it? |
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1d |
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The proportion between permutations and derangements. You can get an exact figure from inclusion-exclusion. The difference is between $1/(N+1)$ and $1/(N+2)$. See en.wikipedia.org/wiki/Derangement |
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1d |
answered | Is there a convenient differential calculus for cojets? |
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2d |
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Is there a convenient differential calculus for cojets? The $k$-jet bundle isn't a vector bundle for $k \geq 2$. The fibers are vector spaces, but the transitions are not linear maps. In particular, it cannot be dual to a co-jet vector bundle. |
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2d |
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What is the algebraic geometry version of the spheres? Out of curiousity, what is the map $\mathbb{P}^1 \times \mathbb{P}^1 \to \mathbb{P}^2$? |
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2d |
answered | Is there a scheme corresponding to the unit interval? |
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2d |
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Are there any very hard unknots? Reply from Panos: Thank you, you are right it seems the quotient knot is trivial. It took me 10 minutes and 10 seconds to prove this. 10 minutes to make the knot using a string (I put the string on top of Dynnikov's example gluing the corners with play dough) and then I tied the ends and lifted this. It took about 10 seconds to unknot but I have no idea what I did. It seems unlikely that I made a mistake as one wrong crossing would make it non trivial I assume. Still I am curious to see your 1st unknotting move as I really don't know what happened after I lifted the knot. |
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Jun 13 |
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derivative of Riemann zeta function Could you provide a brief summary of the result you have in mind? A bare link is rather uninviting. |
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Jun 12 |
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Reference request: Affine Grassmannian and G-bundles @nosr: there is a brief global description of the functor in section 5 (about the commutativity constraint), with no proofs. |
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Jun 11 |
accepted | How to understand the infraconnected set and affinoid? |
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Jun 10 |
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Textbooks on Algorithmic Number Theory William Stein has a book about doing number theory with SAGE. |
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Jun 10 |
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Reference request: Affine Grassmannian and G-bundles There is a description in Mirkovic-Vilonen, but it is missing some details: arxiv.org/abs/math/0401222 |
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Jun 9 |
answered | How to understand the infraconnected set and affinoid? |
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Jun 9 |
answered | Good Computer Package for Calculating Inverse of a Formal Power Series? |
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Jun 9 |
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closed subscheme of ind scheme SGA3 uses the notation $\underline{\operatorname{Hom}}_k(C-x,T)$ to indicate the Hom sheaf. The underline is to keep people from mistaking it for the Hom-set. |
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Jun 9 |
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Formal definitions for a few lattice packing invariants $\min \Lambda$ is the smallest distance between distinct vectors. |
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Jun 7 |
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State of research in moduli space of flat connections The Geometric Langlands Program, which is a reasonably active field, has something to do with sheaves on this moduli space. |
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Jun 7 |
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Bound on the order of a finite group generated by elements $a$ and $b$ of order 2 and $n \geq 3$ such that the sum of the images of $a$, $b$ and $b^{-1}$ under any ordinary representation has only rational eigenvalues @katie, thank you. That is the sort of information that can be helpful when inserted into the text of the question. |
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Jun 7 |
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A question about the $\partial_q$ I don't know $q$-calculus, but is it legal to verify such an identity by post-composing with $\partial_q$, and applying the left and right side to an input like $\partial_q g$? |
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Jun 6 |
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Bound on the order of a finite group generated by elements $a$ and $b$ of order 2 and $n \geq 3$ such that the sum of the images of $a$, $b$ and $b^{-1}$ under any ordinary representation has only rational eigenvalues Do you mean $\tau(a) + \tau(b) + \tau(b^{-1})$? I don't know what you mean by addition in a non-abelian group (although addition in the group ring would yield the above formula). |
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Jun 3 |
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A question on degeneration of elliptic curves with actions. You can think of $C_{reg}$ as a group, because "generalized elliptic curves" come with distinguished identity sections to the smooth locus. |
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Jun 3 |
answered | A question on degeneration of elliptic curves with actions. |
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Jun 2 |
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are these functors exact? I should have said $\mathcal{O}$-modules. |
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Jun 2 |
accepted | are these functors exact? |
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Jun 1 |
answered | are these functors exact? |
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Jun 1 |
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Representation quaternions as matrices Have you looked at en.wikipedia.org/wiki/Quaternion_algebra ? |
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May 31 |
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diffusion equation I've taken the liberty of TeXing the math, but there is a lot of room for improvement. For example, you did not describe the "problem" you had. Also, the level of this question may be somewhat outside the scope of MathOverflow. |
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May 31 |
revised |
diffusion equation TeX repair |
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May 31 |
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Primes for which 2 and -2 are residues. I think this question may be more appropriate at math.stackexchange.com |
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May 31 |
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Degree and Family of Scheme Since each $X_p$ is the intersection of $X$ with the subvariety $\mathbb{P}^{n_1} \times p \subset \mathbb{P}^N$, can't you bound the degree of $X_p$ by a suitable product? |
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May 31 |
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Coordinates on moduli spaces of curves Depending on your definition of "coordinate system" you may be out of luck in most cases, since the moduli spaces transition to general type for large $g$. |
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May 31 |
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Solution of a special class of Diophantine Equations I don't see why you should expect automorphic functions to parametrize arbitrary varieties. If you have a smooth plane curve $P(x,y)=0$ of positive genus, you cannot write $y$ as a function of $x$ without choosing branches. A standard example is $y^2 = x^3+1$, where $y=\pm \sqrt{x^3+1}$ is not really a function of $x$, and is not automorphic (as far as I know). |
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May 30 |
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On a limit involving consecutive primes If you feel the need to change the title of a question, you could at least turn it into a question. |
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May 29 |
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common roots of bivariate polynomial equations You should edit your question, instead of adding a new answer. I've merged the two accounts you created, so it should be possible now. |
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May 29 |
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Do there exist transcendental numbers which are not hypertranscendental? Here is a comment by CofWsug in response to Mark (from a deleted answer): Since $g$ has coefficients in $\mathbb{Q}[i]$, it suffices to write $g=g_1+ig_2$ where $g_1$, $g_2$ are entire functions with rational coefficients, then you can see that $h=g_1−ig_2$. It follows that $gh=g^2_1+g^2_2$ which is obviously an entire function with rational coefficients. |
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May 27 |
answered | Example for non equivalent rational full CFTs with same modular invariant (partition function) |
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May 14 |
answered | References for period matrix of abelian variety |
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May 14 |
answered | What happens to Virasoro at c=25? |
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May 11 |
accepted | A possible consequence of Dirichlet’s theorem about primes in arithmetic progression |
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May 11 |
answered | A possible consequence of Dirichlet’s theorem about primes in arithmetic progression |
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May 11 |
awarded | ● Necromancer |
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May 11 |
answered | japanese/chinese for mathematicians? |
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May 8 |
accepted | Covering of a group by seven proper subgroups: Counterexample |
