MathOverflow

I have recently become interested in diffeologies, and more generally smooth sets, and was interested in the notion of a cobordism between two such objects. In order to define such a concept, one would need a way to define the boundary of a diffeology...

There is a proof that not only is the Halting Problem uncomputable, but there is a total computable function $f$ such that, for all Turing machines $M$, $f(M)$ gives an input where $M$ either fails to halt, or halts and gets gets the Halting Problem...

There is an interesting trick used in Chen-LeBrun-Weber's paper on the extremal Kähler metrics of $\mathbb{CP}^2\#2\overline{\mathbb{CP}^2}$, and I would like to know whether it can be (has been?) exploited further.
The trick applies to certain Kähler classes $\mathfrak{k}$ of a complex manifold $M$, and allows one to give upper and lower bounds for the scalar curvature of an extremal Kähler metric in $\mathfrak{k}$, if such a metric exists. This is important later...

In Corollary 1.5 of this paper, Elkies, Howe, and Ritzenthaler prove that if $C/\mathbb{F}_q$ is a curve of genus $g$ and $g > 510 q^{8\sqrt{q}+3}\log q$, then $\operatorname{Jac}(C)$ cannot be isogenous to a product of elliptic curves.
Now, suppose we specialize to the case where $\operatorname{Jac}(C)$ is isogenous to a power of a supersingular elliptic curve $E/\mathbb{F}_q$. This is equivalent to $C$ being optimal over $\mathbb{F}_{q^2}$, and in this case the maximal possible genus...