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We describe globally nilpotent differential operators of rank 2 defined over a number field whose monodromy group is a nonarithmetic Fuchsian group. We show that these differential operators have an S-integral solution. These differential operators are naturally associated with Teichmueller curves in genus 2. They are counterexamples to conjectures by Chudnovsky--Chudnovsky and Dwork. We also determine the field of moduli of primitive Teichmueller curves in genus 2, and an explicit equation in some cases.
In this paper, we present a different proof on the discrete Fourier restriction. The proof recovers Bourgains level set result on Strichartz estimates associated with Schrodinger equations on torus. Some sharp estimates on $L^{frac{2(d+2)}{d}}$ norm
We compute the Galois groups for a certain class of polynomials over the the field of rational numbers that was introduced by S. Mori and study the monodromy of corresponding hyperelliptic jacobians.
This is a survey article whose main goal is to explain how many components of the character variety of a closed surface are either deformation spaces of representations into the maximal compact subgroup or deformation spaces of certain Fuchsian repre
We prove that $p$-determinants of a certain class of differential operators can be lifted to power series over $mathbb{Q}$. We compute these power series in terms of monodromy of the corresponding differential operators.
We construct the Frobenius structure on a rigid connection $mathrm{Be}_{check{G}}$ on $mathbb{G}_m$ for a split reductive group $check{G}$ introduced by Frenkel-Gross. These data form a $check{G}$-valued overconvergent $F$-isocrystal $mathrm{Be}_{che