4 problems

Compatibility conjecture. The isomorphisms between different moduli spaces given by the middle convolution map preserve the Hodge filtration, the ${\mathbb C}^{\ast}$ action, and t…

Extension conjecture. The formula remains true for arbitrary semisimple $K$ and $L$. The displayed formula is proved in the stated setting where $K$ and $L$ arise from pure pervers…

Let $\bold A=(A^{(0)}_{m_0},\dots,A^{(0)}_1,A^{(1)}_{m_1},\dots,A^{(r)}_0)$ be a tuple of matrices acting on $V$, and let ${\rm idx}(\bold A)$ denote its index of rigidity. Suppose…

Dettweiler–Reiter's middle convolution describes a transformation of regular singular systems, while an irregular singular system may have a pole of arbitrary order at infinity. Ta…