MathOverflow

Let $S$ be a closed surface and $\mathcal M$ be the space of metrics on $S$ equipped with the Lipschitz distance $d$. (Say, up to isometry isotopic to the identity and $d$ is also defined with respect to that.) Pick $k \in \mathbb R$ and let $\mathcal...

Joshua Lederberg received a the Nobel price in medicine in 1958 and he was a major contributor to the Stanford DENDRAL software expert system that
Given a mass spectrum of an organic molecular sample and the chemical formula of the molecule, the program will produce a short list of molecular "graphs" as hypotheses......

For $i\geq 0$, let $A_i$ be a functor from commutative rings to abelian groups satisfying descent for some topology, e.g. Zariski. Let $d_i:A_i\to A_{i+1}$ be a natural transformation such that $d_i\circ d_{i+1}=0$.
This way, we get a functor from commutative rings to cochain complexes$$C=[A_0\xrightarrow{d_0} A_1 \xrightarrow{d_1} A_2 \to \cdots]$$...

Is there a degree-5 polynomial $ p\left(t\right) = a_0 + a_1 \cdot t + a_2 \cdot t^2 + a_3 \cdot t^3 + a_4 \cdot t^4 + a_5 \cdot t^5 $ with integer coefficients $ a_j $, such that $ p\left(t\right) $ is irreducible over rationals, but the second iterate...