10 problems

Differential Galois integrability conjecture. The identity component of the differential Galois group of the $k$-th order variational equations is Abelian for every…

Grothendieck–Katz and Bombieri–Dwork conjectures. The Lie algebra of the differential Galois group of $D$ is minimal with the property that, for almost all primes $\mathfrak p$ of…

A generalised Frenkel–Gross $G$-connection is a connection on the multiplicative group with an irregular singularity at infinity of slope $1/h$ and a regular singularity at $0$. Th…

Let $T$ be a minimal-order telescoper for an integral … where $a$ is algebraic in $x$ and $h$. Finiteness conjecture. If the Galois group of $T$ is virtually solvable, then it is f…

The trivial-Galois-group conjecture. However large $\alpha$, $\beta$, and $r$ are, the Galois group of the associated third-order homogeneous equation is trivial in the category of…

Matzat's conjecture. The absolute differential Galois group of $F$ is the free proalgebraic group on a set of cardinality $|F|$.

Let $\lambda$ and $E$ be the parameters of the axisymmetric Bianchi IX cosmological model, and let $\gamma_1,\gamma_2\in\mathbb{C}$ be the constants appearing in the differential G…

Let $k$ be an algebraically closed field of characteristic zero, set $K=k(x)$ with derivation $d/dx$, and let $F_X$ be the abstract free group on a set $X$ of cardinality $|k|$. A…

Katz's Lie-algebraic $p$-curvature conjecture. With this notation, $\mathfrak g$ is the smallest algebraic Lie subalgebra of $\operatorname{End}_{\mathcal O_X}V\otimes K(X)$ such t…

Let … be the Hamiltonian of the minimally coupled scalar-field system. Assume $\Lambda\ne0$, let $n$ be an integer satisfying … and consider a generic energy level $E\ne0$. Integra…