**Collection Number**C15021

**Collection Date**

**Collection Type**Conference/School

(Mock) Modularity, Moonshine and String Theory

## Traces of Singular Moduli and Moonshine for the Thompson group

Jeffrey Harvey
University of Chicago

We observe a relationship between the representation theory of the Thompson sporadic group and a weakly holomorphic modular form of weight one-half that appears in Zagier's work on traces of singular moduli and Borcherds products. We conjecture the existence of an infinite dimensional graded module for the Thompson group and use the observed relationship to propose a McKay-Thompson series for each conjugacy class of the Thompson group and then construct weakly holomorphic weight one-half forms at higher level that coincide with the proposed McKay-Thompson series.

## TBA

Albrecht Klemm
Rheinische Friedrich-Wilhelms-Universität Bonn

## Symplectic automorphisms of some hyperk\"ahler manifolds

## Moonshine at c=12

Shamit Kachru
Stanford University

## Umbral Moonshine Modules

John Duncan
Case Western Reserve University

Umbral moonshine attaches mock modular forms and meromorphic Jacobi forms to automorphisms of the Niemeier lattices. It is now known that this association can be recovered from specific, graded modules for the Niemeier lattice automorphism groups. We will describe recent progress in a program to realize these modules explicitly.

## U-duality, exotic instantons and automorphic forms on Kac-Moody groups

Daniel Persson
Chalmers University of Technology

## Fricke S-duality in CHL models

Roberto Volpato
Max Planck Institute for Gravitational Physics - Albert Einstein Institute (AEI)

We consider dual pairs of four dimensional heterotic/type IIA CHL models with 16 space-time supersymmetries. We provide strong evidence for the existence of an S-duality acting on the heterotic axion-dilaton by a Fricke involution S --> -1/NS, where N is the order of the orbifold symmetry. While most models are self-dual, in some cases S-duality relates the CHL model to a compactification of type IIA on an orbifold of T^6. We provide a simple criterion to determine whether a model is self-dual or not.

## Optimal Jacobi Forms and Mock Theta Functions

Miranda Cheng
Universiteit van Amsterdam

## How does extended supersymmetry affect the elliptic genus?

Katrin Wendland
Albert-Ludwig Universität Freiburg

The elliptic genus of K3 and its decomposition into characters of the N=4 superconformal algebra of associated conformal field theories can be viewed as the outset of Mathieu Moonshine. Thus, extended supersymmetry induces additional properties of the elliptic genus, which so far lack a satisfactory geometric interpretation. We investigate the implications of this decomposition on geometric structures that underlie the elliptic genus.

## Modular invariance and holographic CFTs

Modular invariance plays an important role in AdS3/CFT2 holography. I discuss the structure of non-holomorphic CFT partition functions, namely in what sense the light spectrum determines the heavy spectrum and how to construct example partition functions using Poincare series. This yields necessary conditions on the spectrum of holographic CFTs. Finally I will discuss permutation orbifolds as examples of such theories.