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 …

A partition of a positive integer n is any nonincreasing sequence of p itive integers whose
sum is n. Let p (n) denote the number of partitions o (as usual, we adopt the convention that …

Together with his collaborators, most notably Kathrin Bringmann and Jan Bruinier, the
author has been researching harmonic Maass forms. These non-holomorphic modular forms …

Fourier transform and the global Gan–Gross–Prasad conjecture for unitary groups Page 1
Annals of Mathematics 180 (2014), 971–1049 http://dx.doi.org/10.4007/annals.2014.180.3.4 …

We study the Faltings height pairing of arithmetic special divisors and CM cycles on Shimura
varieties associated to orthogonal groups. We compute the Archimedean contribution to the …

We prove a new converse theorem for Borcherdsʼ multiplicative theta lift which improves
the previously known results. To this end we develop a newform theory for vector valued …

A bstract Recently, we introduced a new procedure for computing a class of one-loop BPS-
saturated amplitudes in String Theory, which expresses them as a sum of one-loop …

This volume provides a systematic survey of almost all the equivalent assertions to the
functional equations—zeta symmetry—which zeta-functions satisfy, thus streamlining …

Harmonic Maass forms have recently been related to many different topics in number theory:
Ramanujan's mock theta functions, Dyson's rank generating functions, Borcherds products …