Threefold flops, matrix factorisations, and noncommutative algebras

Joseph Karmazyn, University of Sheffield. Part of the pure mathematics algebra seminars series

Threefold flops in algebraic geometry were classified into 6 families by Katz and Morrison using the length invariant. 

Curto and Morrison have also given an efficient and explicit description of the first two families via matrix factorisations, and they conjecture that this can be done generally.

I plan to recap and discuss these results and to explain how the classification can be explicitly realised using noncommutative algebra.