Witten’s seminal 1988 work revealed the connection between 3-dimensional Chern-Simons theory and knot invariants. In this talk, I will provide a physically motivated overview and explain how skein relations manifest from a path-integral/partition-function perspective on 3-manifolds with Wilson lines inserted. There will also be some fun topological brain-twisters for the audience. If time permits, I will comment on recent developments involving factorization homology and its relation to correlators for logarithmic CFTs.

Junior Strings is a seminar series where DPhil students present topics of common interest that do not necessarily overlap with their own research area. This is primarily aimed at PhD students and post-docs but everyone is welcome.

Gaussian fields arise in a variety of contexts in both pure and applied mathematics. While their geometric properties are well understood, their topological features pose deeper mathematical challenges. In this talk, I will begin by highlighting some motivating examples from different domains. I will then outline the classical theory that describes the geometric behaviour of Gaussian fields, before turning to more recent developments aimed at understanding their topology using the Wiener chaos expansion.