相关论文: Monstrous Moonshine: The first twenty-five years
We consider the little-known anthropic argument of Fontenelle dealing with the nature of cometary orbits, given a year before the publication of Newton's Principia. This is particularly interesting in view of the rapid development of the…
This article is an introduction to newly discovered relations between volumes of moduli spaces of Riemann surfaces or super Riemann surfaces, simple models of gravity or supergravity in two dimensions, and random matrix ensembles. (The…
In 2007, Dmytrenko, Lazebnik and Williford posed two related conjectures about polynomials over finite fields. Conjecture~1 is a claim about the uniqueness of certain monomial graphs. Conjecture~2, which implies Conjecture~1, deals with…
This is a significant revision of the early version of this paper which was posted last December. The speculative section has been removed in light of some recent results of Morita and Kawazumi. Numerous typos have been fixed. The companion…
We give a new, simpler proof that the canonical actions of finite groups on Fricke-type Monstrous Lie algebras yield genus zero functions in Generalized Monstrous Moonshine, using a Borcherds-Kac-Moody Lie algebra decomposition due to…
Scientific paper is devoted to establish connection of T-matrix - matrix of composite numbers 6h+1 v 6h-1 in special view - with Legendre's conjecture.
We establish a case of the surprising correlation phenomenon observed in the recent works of He, Lee, Oliver, Pozdnyakov, and Sutherland between Fourier coefficients of families of modular forms and their root numbers.
In fuzzy group theory many versions of the well-known Lagrange's theorem have been studied. The aim of this article is to investigate the converse of one of those results. This leads to an interesting characterization of finite cyclic…
Submanifolds of finite type were introduced by the author during the late 1970s. The first results on this subject were collected in author's books [26,29]. In 1991, a list of twelve open problems and three conjectures on finite type…
We prove a conjecture made by Gilman in 1984 that the groups presented by finite, monadic, confluent rewriting systems are precisely the free products of free and finite groups.
Let G be a semisimple complex algebraic group, and H a wonderful subgroup of G. We prove several results relating the subgroup H to the properties of a combinatorial invariant S of G/H, called its spherical system. It is also possible to…
The Chelyabinsk meteor sailed over skies in a streak of light that was momentarily brighter than the Sun. The Chelyabinsk superbolide is a complex and multi-aspect phenomenon. The Appendix to the book examines the role of cosmic collisions…
The class of convex sets that admit approximations as Minkowski sum of a compact convex set and a closed convex cone in the Hausdorff distance is introduced. These sets are called approximately Motzkin-decomposable and generalize the notion…
Forty-five years ago, a young researcher in finite permutation group theory encountered a paper by Robert Woodrow. The homogeneous triangle-free graph Woodrow described there seemed to be an infinite analogue of the Higman--Sims graph which…
We study replication identities satisfied by conformal characters of a 2D CFT, providing a natural framework for a physics interpretation of the famous Hauptmodul property of Monstrous Moonshine, and illustrate the underlying ideas in…
A wealth of astronomical data indicate the presence of mass discrepancies in the Universe. The motions observed in a variety of classes of extragalactic systems exceed what can be explained by the mass visible in stars and gas. Either (i)…
In this paper we address the following two closely related questions. First, we complete the classification of finite symmetry groups of type IIA string theory on $K3\times \mathbb R^6$, where Niemeier lattices play an important role. This…
The D1-D5-KK-p system naturally provides an infinite dimensional module graded by the dyonic charges whose dimensions are counted by the Igusa cusp form, Phi_{10}(Z)$. We show that the Mathieu group, M_{24}, acts on this module by…
We generalize the "miraculous cancellation" formulas of Alvarez-Gaum\'e, Witten and Kefeng Liu to a twisted version where an extra complex line bundle is involved. We also apply our result to discuss intrinsic relations between the higher…
These lecture notes explain the construction and basic properties of the wonderful compactification of a complex semisimple group of adjoint type. An appendix discusses the more general case of a semisimple symmetric space.