相关论文: Icosahedron, exceptional singularities and modular…

The moduli stack M_X(E_8) of principal E_8-bundles over a smooth projective curve X carries a natural divisor Delta. We study the pull-back of the divisor Delta to the moduli stack M_X(P), where P is a semi-simple and simply connected group…

In this paper, we study the (anti-)self-duality equations $\ast F\wedge F=\pm F\wedge F$ in the eight-dimensional Euclidean space. Using properties of the Clifford algebra $Cl_{0,8}(\mathbb{R})$, we find a new solution to these equations.

In this talk we present some links of the theory of the odderon with elliptic curves. These results were obtained in an earlier work \cite{RJ}. The natural degrees of freedom of the odderon turn out to coincide with conformal invariants of…

We give a construction that takes a simple linear algebraic group $G$ over a field and produces a commutative, unital, and simple non-associative algebra $A$ over that field. Two attractions of this construction are that (1) when $G$ has…

We consider the isomonodromy problems for flat $G$-bundles over punctured elliptic curves $\Sigma_\tau$ with regular singularities of connections at marked points. The bundles are classified by their characteristic classes. These classes…

We find a natural $L_{\omega_1,\omega}$-axiomatisation $\Sigma$ of a structure on the upper half-plane $\mathbb{H}$ as the covering space of modular curves. The main theorem states that $\Sigma$ has a unique model in every uncountable…

A conjecture in [Ish20] states that for a finite subgroup $G$ of $GL(2; \mathbb{C})$, a resolution $Y$ of $\mathbb{C}^2/G$ is isomorphic to a moduli space $\mathcal{M}_{\theta}$ of $G$-constellations for some generic stability parameter…

Based on an interpretation of the quark-lepton symmetry in terms of the unimodularity of the color group $SU(3)$ and on the existence of 3 generations, we develop an argumentation suggesting that the "finite quantum space" corresponding to…

We obtain a novel connection between the exact solutions of the plane pendulum, hyperbolic plane pendulum and inverted plane pendulum equations as well as the static solutions of the sine-Gordon and the sine hyperbolic-Gordon equations and…

It is well known that the point group of the root lattice D_6 admits the icosahedral group as a maximal subgroup. The generators of the icosahedral group H_3, its roots and weights are determined in terms of those of D_6. Platonic and…

We consider static spherically symmetric solutions of Einstein's equations coupled to an SU(2) Yang Mills field that are smooth at the center of spherical symmetry. We prove that with small cosmological constant there exist solutions that…

There are many ways to embed the Lie groups of the Standard Model of Particle Physics in a Lie group of type $E_8$, but so far there is no convincing demonstration that the finite symmetries (and asymmetries) of weak hypercharge, three…

We introduce a new class of solutions to Laplace equation, dubbed logopoles, and use them to derive a new relation between solutions in prolate spheroidal and spherical coordinates. The main novelty is that it involves spherical harmonics…

We examine the moduli space E=T* of complex tori T(t)=C/L(t) where L(t)=cost.n(t)Lt. We find that the Dedekind eta function furnishes a bridge between the euclidean and hyperbolic structures on T*=C-L/L as well as between the doubly…

Exceptional modular invariants for the Lie algebras B2 (at levels 2,3,7,12) and G2 (at levels 3,4) can be obtained from conformal embeddings. We determine the associated alge bras of quantum symmetries and discover or recover, as a…

This paper is a sequel to [He7]. There a notion of marking of isolated hypersurface singularities was defined, and a moduli space $M_\mu^{mar}$ for marked singularities in one $\mu$-homotopy class of isolated hypersurface singularities was…

Regular polytopes, the generalization of the five Platonic solids in 3 space dimensions, exist in arbitrary dimension $n\geq-1$; now in {\rm dim}. 2, 3 and 4 there are \emph{extra} polytopes, while in general dimensions only the…

Using a geometric realization of the $SU(2)_R$ symmetry and a procedure of factorisation of the gauge and $SU(2)_R$ charges, we study the small instanton singularities of the Higgs branch of supersymmetric $U(1)^r$ gauge theories with eight…

In this article we introduce Hecke operators on the differential algebra of geometric quasi-modular forms. As an application for each natural number $d$ we construct a vector field in six dimensions which determines uniquely the polynomial…

We notice that one of the Diophantine equations, $knm=2kn+2km+2nm$, arising in the universality originated Diophantine classification of simple Lie algebras, has interesting interpretations for two different sets of signs of variables. In…