Claudia Scheimbauer - En-algebras, extended topological field theories and dualizability
The Cobordism Hypothesis provides a beautiful interplay between extended topological field theories and dualizability conditions, allowing for a conceptual explanation of certain finiteness conditions appearing in representation theory, and, vice versa, a geometric understanding of algebraic objects. In turn, En-algebras, which are algebras for the little disks operad, (e.g. associative algebras and quantum groups) provide important examples. I will explain why every En-algebra leads to a categorified topological field theory using dualizability arguments. Furthermore, I will explore extensions and further directions.