Dr Jan Dobrowolski (University of Leeds) gives a maths seminar at the School of Mathematics, UEA. The talk is on “Independence in vector spaces with a bilinear form”. The abstract is below.

NSOP1 is a property of first-order structures which can be characterised by existence of an independence relation satisfying certain natural properties. Infinite dimensional vector spaces over algebraically closed fields equipped with a non-degenerate bilinear form are among the main examples of NSOP1 structures. Using this class of structures as an example, I will explain the model-theoretic concepts and phenomena occurring in NSOP1 theories. If time permits, I will also discuss groups definable in these structures.