相关论文: Modular Invariants and Generalized Halphen Systems
We investigate global solvability, in the framework of smooth functions and Schwartz distributions, of certain sums of squares of vector fields defined on a product of compact Riemannian manifolds $T \times G$, where $G$ is further assumed…
We model generalized harmonic functions on rings of differential operators and complex function spaces. The differential operators in the second Weyl-algebra that commute with rotations are described and leads to a natural notion for such…
We construct the meromorphic functions invariant under the action of the sense-preserving wallpaper groups on the complex plane. We discuss possible generalisa-tions of this to the general wallpaper groups. This provides the answer to a…
We show that a collection of generalized Bowen-Franks group, what we call the principal Bowen-Franks $R$-modules, form a complete set of $R$-module invariants for the equivalence relation of profinite conjugacy for similar hyperbolic toral…
Modular graph forms (MGFs) are a class of non-holomorphic modular forms which naturally appear in the low-energy expansion of closed-string genus-one amplitudes and have generated considerable interest from pure mathematicians. MGFs satisfy…
The bases of the theory of integrals for multidimensional differential systems are stated. The integral equivalence of total differential systems, linear homogeneous systems of partial differential equations, and Pfaff systems of equations…
We classify quasilinear systems in Riemann invariants whose characteristic webs are linearizable on every solution. Although the linearizability of an individual web is a rather nontrivial differential constraint, the requirement of…
We introduce a natural generalisation of holomorphic curves to morphisms of supermanifolds, referred to as holomorphic supercurves. More precisely, supercurves are morphisms from a Riemann surface, endowed with the structure of a…
In this paper, we derive a "hamiltonian formalism" for a wide class of mechanical systems, including classical hamiltonian systems, nonholonomic systems, some classes of servomechanism... This construction strongly relies in the geometry…
The purpose of this paper is to generalise Sullivan's rational homotopy theory to non-nilpotent spaces, providing an alternative approach to defining Toen's schematic homotopy types over any field k of characteristic zero. New features…
A detailed proof is given of a theorem describing the centraliser of a transitive permutation group, with applications to automorphism groups of objects in various categories of maps, hypermaps, dessins, polytopes and covering spaces, where…
First we survey and explain the strategy of some recent results that construct holomorphic $\text{sl}(2, \mathbb C)$-differential systems over some Riemann surfaces $\Sigma_g$ of genus $g\geq 2$, satisfying the condition that the image of…
Ultrafunctions are a particular class of generalized functions defined on a hyperreal field $\mathbb{R}^{*}\supset\mathbb{R}$ that allow to solve variational problems with no classical solutions. We recall the construction of ultrafunctions…
Let G be a finite connected simple graph. We define the moduli space of conformal structures on G. We propose a definition of conformally covariant operators on graphs, motivated by [25]. We provide examples of conformally covariant…
Differentially positive systems are the nonlinear systems whose linearization along trajectories preserves a cone field on a smooth Riemannian manifold. One of the embryonic forms for cone fields in reality is originated from the general…
Motivated by a question of Rubel, we consider the problem of characterizing which noncompact hypersurfaces in $\RR^n$ can be regular level sets of a harmonic function modulo a $C^\infty$ diffeomorphism, as well as certain generalizations to…
General solutions of relativistic wave equations are studied in terms of the functions on the Lorentz group. A close relationship between hyperspherical functions and matrix elements of irreducible representations of the Lorentz group is…
For many finite groups, the Inverse Galois Problem can be approached through modular/automorphic Galois representations. This is a report explaining the basic strategy, ideas and methods behind some recent results. It focusses mostly on the…
The concept and the construction of modular graph functions are generalized from genus-one to higher genus surfaces. The integrand of the four-graviton superstring amplitude at genus-two provides a generating function for a special class of…
The classical Green's function associated to a simply connected domain in the complex plane is easily expressed in terms of a Riemann mapping function. The purpose of this paper is to express the Green's function of a finitely connected…