S. Carnahan

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 Name S. Carnahan Member for 3 years Seen 2 hours ago Website Location 筑波市, Japan Age
I think this is a neat project.
 2h comment Examples of interesting false proofsI 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? 4h answered Is there a topograph for Pythagorean triples? 4h comment 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 $d^2z = -\frac{2}{w^3} (dw)^2 - \frac{1}{w^2}d^2w$. 14h comment And old hat with a new plumeHow well does this reasoning work when there are only one or two islanders? 17h awarded ● Nice Answer 1d answered The proportion between permutations and derangements. 1d comment 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. 1d comment Functions about integers which are divisible by all numbers less than or equal to a fractional power of the integerWhat do you want to do with this function, aside from defining it? 1d comment 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 1d answered Is there a convenient differential calculus for cojets? 2d comment 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. 2d comment What is the algebraic geometry version of the spheres?Out of curiousity, what is the map $\mathbb{P}^1 \times \mathbb{P}^1 \to \mathbb{P}^2$? 2d answered Is there a scheme corresponding to the unit interval? 2d comment 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. Jun13 comment derivative of Riemann zeta functionCould you provide a brief summary of the result you have in mind? A bare link is rather uninviting. Jun12 comment 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. Jun11 accepted How to understand the infraconnected set and affinoid? Jun10 comment Textbooks on Algorithmic Number TheoryWilliam Stein has a book about doing number theory with SAGE. Jun10 comment 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 Jun9 answered How to understand the infraconnected set and affinoid? Jun9 answered Good Computer Package for Calculating Inverse of a Formal Power Series? Jun9 comment closed subscheme of ind schemeSGA3 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. Jun9 comment Formal definitions for a few lattice packing invariants$\min \Lambda$ is the smallest distance between distinct vectors. Jun7 comment State of research in moduli space of flat connectionsThe Geometric Langlands Program, which is a reasonably active field, has something to do with sheaves on this moduli space. Jun7 comment 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. Jun7 comment 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 $\partial_q g$? Jun6 comment 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 eigenvaluesDo 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). Jun3 comment 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. Jun3 answered A question on degeneration of elliptic curves with actions. Jun2 comment are these functors exact?I should have said $\mathcal{O}$-modules. Jun2 accepted are these functors exact? Jun1 answered are these functors exact? Jun1 comment Representation quaternions as matricesHave you looked at en.wikipedia.org/wiki/Quaternion_algebra ? May31 comment diffusion equationI'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. May31 revised diffusion equationTeX repair May31 comment Primes for which 2 and -2 are residues.I think this question may be more appropriate at math.stackexchange.com May31 comment Degree and Family of SchemeSince 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? May31 comment Coordinates on moduli spaces of curvesDepending 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 $g$. May31 comment Solution of a special class of Diophantine EquationsI 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). May30 comment On a limit involving consecutive primesIf you feel the need to change the title of a question, you could at least turn it into a question. May29 comment common roots of bivariate polynomial equationsYou should edit your question, instead of adding a new answer. I've merged the two accounts you created, so it should be possible now. May29 comment 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. May27 answered Example for non equivalent rational full CFTs with same modular invariant (partition function) May14 answered References for period matrix of abelian variety May14 answered What happens to Virasoro at c=25? May11 accepted A possible consequence of Dirichlet’s theorem about primes in arithmetic progression May11 answered A possible consequence of Dirichlet’s theorem about primes in arithmetic progression May11 awarded ● Necromancer May11 answered japanese/chinese for mathematicians? May8 accepted Covering of a group by seven proper subgroups: Counterexample