Related papers: Generalized Lam\'e equation with finite monodromy

Let X be a 2-sphere with n punctures. We classify all conjugacy classes of Zariski-dense representations $$\rho: \pi_1(X)\to SL_2(\mathbb{C})$$ with finite orbit under the mapping class group of X, such that the local monodromy at one or…

The Darboux-Treibich-Verdier (DTV) potential $\sum_{k=0}^{3}n_{k}(n_{k}+1)\wp(z+\tfrac{ \omega_{k}}{2};\tau)$ is well-known as doubly-periodic solutions of the stationary KdV hierarchy (Treibich-Verdier, Duke Math. J. {\bf 68} (1992),…

Suppose $\rho_1, \rho_2$ are two $\ell$-adic Galois representations of the absolute Galois group of a number field, such that the algebraic monodromy group of one of the representations is connected and the representations are locally…

In this paper we define (special) GLIT classes and (special) GLIT algebras. We prove that GLIT algebras, which generalise Lat-Igusa-Todorov algebras, satisfy the finitistic dimension conjecture and give several properties and examples. In…

A Generalized Inoue--Bombieri (GIB) manifold $M$ is a compact quotient of a connected Riemannian product $\mathbb{R}^q \times (N,g _N)$ by a discrete subgroup of $\mathrm{Sim}(\mathbb{R}^q) \times \mathrm{Isom}(N,g_N)$. The flat factor…

Pursuing a generalization of group symmetries of modular categories to category symmetries in topological phases of matter, we study linear Hopf monads. The main goal is a generalization of extension and gauging group symmetries to category…

We present general reduction procedures for Courant, Dirac and generalized complex structures, in particular when a group of symmetries is acting. We do so by taking the graded symplectic viewpoint on Courant algebroids and carrying out…

A classical result of F.Klein states that, given a finite primitive group $G\subseteq SL_2(\mathbb{C})$, there exists a hypergeometric equation such that any second order LODE whose differential Galois group is isomorphic to $G$ is…

We introduce a generalized forward-backward splitting method with penalty term for solving monotone inclusion problems involving the sum of a finite number of maximally monotone operators and the normal cone to the nonempty set of zeros of…

Some sorts of generalized morphisms are defined from very basic mathematical objects such as sets, functions, and partial functions. A wide range of mathematical notions such as continuous functions between topological spaces, ring…

We present an extension of the methods of classical Lie group analysis of differential equations to equations involving generalized functions (in particular: distributions). A suitable framework for such a generalization is provided by…

In this article we investigate the existence of a solution to a semilinear, elliptic, partial differential equation with distributional coefficients and data. The problem we consider is a generalization of the Lichnerowicz equation that one…

We study algebraic isomonodromic deformations of flat logarithmic connections on the Riemann sphere with $n\geq 4$ poles, for arbitrary rank. We introduce a natural property of algebraizability for the germ of universal deformation of such…

The aim of this work is to provide a construction of generalized local symbols on algebraic curves as morphisms of group schemes. From a closed point of a complete, irreducible and non-singular curve $C$ over a perfect field $k$ as the only…

This paper provides a realization of all classical and most exceptional finite groups of Lie type as Galois groups over function fields over F_q and derives explicit additive polynomials for the extensions. Our unified approach is based on…

Preliminary group classification became prominent as an approach to symmetry analysis of differential equations due to the paper by Ibragimov, Torrisi and Valenti [J. Math. Phys. 32, 2988-2995] in which partial preliminary group…

We introduce new times in the monodromy preserving equations. While the usual times related to the moduli of complex structures of Riemann curves such as coordinates of marked points, we consider the moduli of generalized complex structures…

In symplectic topology one uses elliptic methods to prove rigidity results about symplectic manifolds and solutions of Hamiltonian equations on them, where the most basic example is given by geodesics on Riemannian manifolds. Harmonic maps…

Finite symmetries abound in particle physics, from the weak doublets and generation triplets to the baryon octet and many others. These are usually studied by starting from a Lie group, and breaking the symmetry by choosing a particular…

We study generalized sums of linear orders. These are binary operations that, given linear orders $A$ and $B$, return an order $A \oplus B$ that can be decomposed as an isomorphic copy of $A$ interleaved with a copy of $B$. We show that…