7 problems

A Ricci-flat ALE instanton is a complete Riemannian manifold with vanishing Ricci curvature and asymptotically locally Euclidean geometry, approaching $\mathbb{R}^4/\Gamma$ at infi…

Let ${\mathcal E}(\mathcal N^\bullet)$ be the eigenvariety constructed from the cohomological complex $\mathcal N^\bullet$ for $\operatorname{GL}_n/\mathbb Q$, and let a cuspidal c…

A self-dual geometric configuration is a geometric configuration equipped with a duality mapping its points and lines to one another; its rank is the order of the self-duality. Grü…

Let … where $(c,d,e)=(j,1+(j-2)m,(j-3)m)$, with $j\geqslant 5$ and $m\geqslant 1$. These lattice configurations define smooth centrally symmetric toric surfaces: for $j=5$ and…

Let $r_n$ be the number of self-dual interval orders of size $n$, and let $q_n$ be the number of primitive self-dual interval orders of size $n$. Size asymptotic conjecture. … with…

A self-dual T-motive is a T-motive admitting a duality with itself. The existence conjecture for other self-dual T-motives. There exist self-dual T-motives $M$, distinct from those…

Let $M$ be the T-motive defined by $Te_* = \theta e_*+A\tau e_*+\tau^2e_*$ with $A\in M_2(\mathbb C_\infty)$, and let $\alpha:M\to M'$ be a constant duality map satisfying…