# All Questions

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### What was achieved on IUT summit, RIMS workshop?

I would like to know what was achieved in the workshop towards the verification of abc conjecture's proof and the advance of understanding of IUT in general. A comment from a participant: C ...
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### Differentiation with composite, product and quotient rule [on hold]

This is a simple question but I hope someone can give a detailed explanation of how to solve the question. Differentiate y=xtan√x.
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### Injectivity of the Chern character in $K$-homology

Let $(\pi,H,F)$ be a Fredholm module: here $\pi:A \to B(H)$ is a representation of an algebra on the Hilbert space $H$ and $F$ is a self adjoint operator with square one such that for each $a \in A$ ...
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### show that $\lim_{|y|\to\infty}|y|^{n-2}u(y)>0$ [on hold]

For $n\geq 3$.Let $u\in C^2(R^n), \Delta u\leq 0,u>0$ in $R^n$, show that $\lim_{|y|\to\infty}|y|^{n-2}u(y)>0$. I was reading the article <Liouville-type theorems and Harnack-type ...
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### For which finite groups $G$ is every character a virtual permutation character?

Let $G$ be a finite group. A (complex) character $\chi$ of $G$ is said to be a virtual permutation character if it can be expressed as a $\mathbb{Z}$-linear combination of characters induced from the ...
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### Singular locus of codimension 1 for a hypersurface [on hold]

If $V$ is a hypersurface and it is reducible, then I know that $\dim Sing(V)= \dim V-1$. Is the contrary true? I.e., if $\dim Sing(V)= \dim V-1$, then $V$ is reducible? I am only interested in ...
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### A (second-order) axiomatic characterization of the integers which rules out surreal/hyperreal versions

I've seen it stated, for example here, that the integers are the unique commutative ordered ring with identity whose positive elements are well-ordered. I understand why the integers are the ...
### Importance of $E_n$-algebras over ring structures on $\pi_*(E)$
Hopefully this question is not too vague to be closed. I am looking for examples of when a construction/theorem that involves $E$-(co)homology or even simply the ring $E_*$ requires an understanding ...