4 problems

Let $C$ be a smooth projective curve over $\mathbb{C}$, and let $D\subset C$ be a reduced effective divisor. A parabolic Higgs bundle over $(C,D)$ is called periodic when it is per…

Assume $R=\mathbb{C}[[x]][y]/(f)$ defines a generically separable degree-$n$ cover of the $x$-axis, fully ramified at the origin. For an integer composition $\nu$ of $n$, let…

Extension conjecture. Theorem, Theorem, and Theorem hold for all compositions $\alpha$.

Let $M$ be a real-analytic connected holomorphically nondegenerate CR-hypersurface of CR-dimension $n$, and let $\mathfrak{s}(M)$ denote its symmetry algebra. Beloshapka's conjectu…