I'll introduce the mathematics of supersymmetry, explaining both the "physical" intuition as well as how super mathematics arises from the world of tensor categories. After such generalities, I'll delve into a developing analogy between supergroups over the complex numbers and the modular representations of finite groups. In particular, it is possible to define the notion of a Sylow subgroup, as well as the analogue of a p-group, in the super setting. This opens up the possibility of applying a wealth of techniques developed for finite groups in the super setting. Part of joint works with Julia Pevtsova, Vera Serganova, and Dmitry Vaintrob.
The talk will be accessible to a broad audience, although a bit of finite group theory will be assumed.