Associative submanifolds in Joyce’s generalised Kummer construction

Início: 20/05/2022 17:00

Término: 20/05/2022 18:00

Palestrante: Shubham Dwivedi (Humboldt University, Berlin)

E-mail do Palestrante: dwivedi.1301@gmail.com

Resumo: Associative submanifolds are special 3-dimensional manifolds in $mathrm{G_2}$ manifolds which are 7-dimensional. They are examples of calibrated submanifolds and there is a research programme that attempts to count them in order to define numerical invariants of $mathrm{G_2}$ manifolds, similar to Gromov-Witten invariants. However the scarcity of examples of associative submanifolds makes it difficult to work out the details of this programme. In the talk I will explain how to construct associatives in $mathrm{G_2}$ manifolds constructed by Joyce, whose existence had previously been predicted by physicists. The talk is based on a joint work with Daniel Platt (King's College London) and Thomas Walpuski (Humboldt University, Berlin).