相关论文: Icosahedron, exceptional singularities and modular…

Tilting objects play a key role in the study of triangulated categories. A famous result due to Iyama and Takahashi asserts that the stable categories of graded maximal Cohen-Macaulay modules over quotient singularities have tilting…

We study special cycles on a Shimura variety of orthogonal type over a totally real field of degree $d$ associated with a quadratic form in $n+2$ variables whose signature is $(n,2)$ at $e$ real places and $(n+2,0)$ at the remaining $d-e$…

In this paper we generalize the idea of "essentially unique" representations by ternary quadratic forms. We employ the Siegel formula, along with the complete classification of imaginary quadratic fields of class number less than or equal…

In this paper, we investigate semilinear elliptic equations with general exponential-type nonlinearities in two dimensions. For such nonlinearities, we establish two main results. The first is the construction of a singular solution.…

From a general metric for stationary cyclic symmetric gravitational fields coupled to Maxwell electromagnetic fields within the $(2+1)$-dimensional gravity the uniqueness of wide families of exact solutions is established, among them, all…

We consider the four-dimensional reduced quasi-classical self-dual Yang--Mills equation and show that non-triviality of the second exotic cohomology group of its symmetry algebra implies existence of a two-component integrable…

We notice a remarkable connection between Bazhanov-Sergeev solution of Zamolodchikov tetrahedron equation and certain well-known cluster algebra expression. The tetrahedron transformation is then identified with a sequence of four…

We introduce an abstract notion of a 3D-rotation module for a group $G$ that does not require the module to carry a vector space structure, a priori nor a posteriori. We prove that, under an expected irreducibility-like assumption, the only…

We use the octonion algebra to construct singular solutions of Hessian fully nonlinear uniformly elliptic equations in 21 or more dimensions. The regularity of these solutions is the least possible one. The same is proven for Isaacs…

We give a new method for constructing vector-valued modular forms from singular scalar-valued ones. As an application we prove the identity between two remarkable spaces of vector-valued modular forms which seem to be unrelated at a first…

We study the instanton partition functions of two well-known superconformal field theories with mass deformations. Two types of anomaly equations, namely, the modular anomaly and holomorphic anomaly, have been discovered in the literature.…

We study second-order modular differential equations whose solutions transform equivariantly under the modular group. In the reducible case, we construct all such solutions using an explicit ansatz involving Eisenstein series and the…

In this paper we construct the quasi regular polyhedra and their duals which are the generalizations of the Archimedean and Catalan solids respectively. This work is an extension of two previous papers of ours which were based on the…

We count the number of isogeny classes of Edwards curves over finite fields, answering a question recently posed by Rezaeian and Shparlinski. We also show that each isogeny class contains a {\em complete} Edwards curve, and that an Edwards…

We show that the two sets of self-dual Yang-Mills equations in 8-dimensions proposed in (E.Corrigan, C.Devchand, D.B.Fairlie and J.Nuyts, {\it Nuclear Physics} {\bf B214}, 452-464, (1983)) form respectively elliptic and overdetermined…

There are a number of publications on relativistic objects dealing either with black holes or naked singularities in the center. Here we show that there exist static spherically symmetric solutions of Einstein equations with a strongly…

We examine the blow-up claims of the incompressible Euler equations for several specific flow-fields, (1) the columnar eddies in the vicinity of stagnation; (2) a quasi-three-dimensional structure for illustrating oscillations and…

We study the classical solutions of the Einstein-Yang-Mills model in five dimensions in the presence of a cosmological constant $\Lambda$. Using a spherically symmetric ansatz and assuming that the fields do not depend on the extra…

We establish an interesting connection between Morin singularities and stable homotopy groups of spheres. We apply this connection to computations of cobordism groups of certain singular maps. The differentials of the spectral sequence…

We prove the existence of exotic but homotopically trivial contact structures on spheres of dimension 8k-1. Together with previous results of Eliashberg and the second author this establishes the existence of such structures on all…