Kolloquium Wilhelm Killing: Prof. Dr. Katrin Wendland (Universität Freiburg): Moonshine Phenomena
Thursday, 11.07.2019 16:30 im Raum M5
Moonshine', in Mathematics, refers to surprising and deep connections
between finite group theory and the theory of so-called modular forms.
The first known instance of Moonshine is Monstrous Moonshine, where the
coefficients of the modular j-function are identified as dimensions of representations
of the Monster group. This was first observed by John McKay in 1987; Richard
Borcherds received a Fields Medal for his proof of the resulting Moonshine
Conjectures in 1998. More than a decade later, Tohru Eguchi, Hiroshi Ooguri
and Yuji Tachikawa proposed 'Mathieu Moonshine', which links the largest
Mathieu group to topological invariants of K3 surfaces, yielding the Fourier
coefficients of a certain elliptic modular form. Conformal field theory turns
out to be key to every known instance of moonshine.
The talk will give an introduction to solved and unsolved mysteries of these
two types of Moonshine.