# String Theory Seminar

### 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.