Monstrous moonshine relates distinguished modular functions to the representation theory
of the Monster. The celebrated observations that 1= 1, 196884= 1+ 196883, 21493760= 1+ …

A bstract We find and propose an explanation for a large variety of modularity-related
symmetries in problems of 3-manifold topology and physics of 3d\(\mathcal {N}\)= 2 theories …

We describe surprising relationships between automorphic forms of various kinds, imaginary
quadratic number fields and a certain system of six finite groups that are parameterised …

Abstract Eguchi, Ooguri and Tachikawa observed that the coefficients of the elliptic genus of
type II string theory on K3 surfaces appear to be dimensions of representations of the largest …

A close relationship between K3 surfaces and the Mathieu groups has been established in
the last century. Furthermore, it has been observed recently that the elliptic genus of K3 has …

A bstract A classical result from analytic number theory by Rademacher gives an exact
formula for the Fourier coefficients of modular forms of non-positive weight. We apply similar …

What follows is a broad-brush overview of the recent synergistic interactions between
mathematics and theoretical physics of quantum field theory and string theory. The …

A bstract We investigate the constraints of crossing symmetry on CFT correlation functions.
Four point conformal blocks are naturally viewed as functions on the upper-half plane, on …

We exhibit an action of Conway's group–the automorphism group of the Leech lattice–on a
distinguished super vertex operator algebra, and we prove that the associated graded trace …

The Mathieu twisted twining genera, ie the analogues of Norton's generalised Moonshine
functions, are constructed for the elliptic genus of K3. It is shown that they satisfy the …