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Daniel Persson, Chalmers University of Technology

Mathieu moonshine, Siegel modular forms and \(N=4\) dyons

In mathematics and physics the word *Moonshine*
represents surprising and deep connections between a priori
unrelated fields, such as number theory, representation theory and
string theory. The most famous example is *Monstrous
Moonshine*, which relates Fourier coefficients of modular forms
with representations of the largest finite sporadic group, known as
the Monster group. Recently, a new moonshine phenomenon was
discovered, which connects the largest Mathieu group \(M24\) with
superconformal field theories on \(K3\)-surfaces. In this talk I
will describe recent progress in our understanding of this *
Mathieu Moonshine*, and show how it is connected to the problem
of counting dyonic black holes in \(N=4\) string theories.