5 problems

Sabbah's conjecture. There is a finite sequence of point blow-ups

Let $I_{3,m}$ be an irregular singularity with $\gcd(3,m)=0$. Write $m=3j+k$ with $k=1,2$, let $q$ and $t$ be the index parameters, and let $\delta_{k,1}$ be the Kronecker delta. C…

Let $I_{2,2m}$ be an irregular singularity, let $\lambda$ label a representation, let $a$ be a flavor fugacity, and let $t$ be the Macdonald parameter. Song's scaling conjecture. T…

Let $I_{2,2m-1}$ be an irregular singularity with $m\geq 1$, let $\lambda$ label the wavefunction, and let $t$ be the Macdonald parameter. Song's conjecture. The wavefunction is ……

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…