Related papers: Computing algebraic Belyi functions on Bring's cur…

This is a first part of a series of papers in which we develop explicit computational methods for automorphic forms for GL(3) and PGL(3) over elliptic function fields. In this first part, we determine explicit formulas for the action of the…

We give a moduli interpretation to the quotient of (nondegenerate) binary cubic forms with respect to the natural $\text{GL}_2$-action on the variables. In particular, we show that these $\text{GL}_2$ orbits are in bijection with pairs of…

We calculate two Belyi pairs using the properties of Mulase-Penkava differential. Details are provided including accurate construction of coordinates, variables and equations. The calculation is a part of the work which results in a…

We employ the functional renormalization group approach formulated on the Schwinger-Keldysh contour to calculate real-time correlation functions in scalar field theories. We provide a detailed description of the formalism, discuss suitable…

Let $\L_g^G$ denote the locus of hyperelliptic curves of genus $g$ whose automorphism group contains a subgroup isomorphic to $G$. We study spaces $\L_g^G$ for $G \iso \Z_n, \Z_2{\o}\Z_n, \Z_2{\o}A_4$, or $SL_2(3)$. We show that for $G \iso…

We show how to speed up the computation of isomorphisms of hyperelliptic curves by using covariants. We also obtain new theoretical and practical results concerning models of these curves over their field of moduli.

We discuss several arithmetic aspects of Bianchi groups, especially from a computational point of view. In particular, we consider computing the homology of Bianchi groups together with the Hecke action, connections with automorphic forms,…

Pull-back transformations between Heun and Gauss hypergeometric equations give useful expressions of Heun functions in terms of better understood hypergeometric functions. This article classifies, up to Mobius automorphisms, the coverings…

We study Severi curves parametrizing rational bisections of elliptic fibrations associated to general pencils of plane cubics. Our main results show that these Severi curves are connected and reduced, and we give an upper bound on their…

We obtain the structure of weight 2 blocks and [2:1]-pairs of q-Schur algebras, and compute explicitly the modular Alvis-Curtis duality for weight 2 blocks of finite general linear groups in non-defining characteristic.

We find the automorphism group of the moduli space of parabolic bundles on a smooth curve (with fixed determinant and system of weights). This group is generated by: automorphisms of the marked curve, tensoring with a line bundle, taking…

We classify, up to isomorphism, the 2-dimensional algebras over a field K. We focuse also on the case of characteristic 2, identifying the matrices of GL(2,F_2) with the elements of the symmetric group S_3. The classification is then given…

In recent work, we demonstrated that a spectral variety for the Berry connection of a 2d $\mathcal{N}=(2,2)$ GLSM with K\"ahler vacuum moduli space $X$ and abelian flavour symmetry is the support of a sheaf induced by a certain action on…

This paper focuses on the derivations and automorphism groups of certain finite-dimensional associative algebras over the field of complex numbers. Using classification results for algebras of dimensions two, three, and four, along with…

For an algebraically closed field K, let G be a finite abelian group of K-linear automorphisms of a finite-dimensional algebra A and AG is the associated skew group algebra. The author with S. Trepode and A. G. Chaio introduced the notion…

We apply a reduction to the Beauville systems to obtain a family of new algebraic completely integrable systems, related to curves with a cyclic automorphism.

In the present paper, we introduce two-dimensional categorified Hall algebras of smooth curves and smooth surfaces. A categorified Hall algebra is an associative monoidal structure on the stable $\infty$-category…

The goal of this paper is to demonstrate the use of techniques from hyperbolic geometry to compute generating sets of certain subgroups of $SL^+(2,\mathbb{C})$; specifically, $SO^+(Q,\mathbb{Z})$ for $Q$ some integral quadratic form of…

We give two congruence properties of Hermitian modular forms of degree 2 over $\mathbb{Q}(\sqrt{-1})$ and $\mathbb{Q}(\sqrt{-3})$. The one is a congruence criterion for Hermitian modular forms which is generalization of Sturm's theorem.…

We discuss various lifting and reduction problems for bundles and gerbes in the context of a strict Lie 2-group. We obtain a geometrical formulation (and a new proof) for the exactness of Breen's long exact sequence in non-abelian…