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Connections between representation categories of quantum groups and vertex operator algebras (VOAs) have been studied since the 1990s starting with the pioneering work of Kazhdan and Lusztig. Recently, connections have been found between unrolled quantum groups and certain families of VOAs. In this talk, I will introduce unrolled quantum groups and describe their connections to the Singlet, Triplet, and Bp vertex operator algebras.

Factorization algebras provide a flexible language for describing the observables of a perturbative QFT, as shown in joint work with Kevin Costello. In joint work with Eugene Rabinovich and Brian Williams, we extend those constructions to a manifold with boundary for a special class of theories that includes, as an example, a perturbative version of the correspondence between chiral U(1) currents on a Riemann surface and abelian Chern-Simons theory on a bulk 3-manifold. Given time, I'll sketch a systematic higher dimensional version for higher abelian CS theory on an oriented smooth manifold of dimension 4n+3 with boundary a complex manifold of complex dimension 2n+1. (This talk will be very informal.)

I will start with an introduction into the framework of perturbative algebraic quantum field theory (pAQFT), which is a mathematically rigorous approach to perturbative QFT. In its original formulation, it is based on the Haag-Kastler axiomatic framework, where locality is a fundamental principle. In my talk I will discuss how it can be extended to treat also non-local observables, with potential applications to effective quantum gravity

Thus far, the non-linear regime of structure formation is only accessible through expensive numerical N-body simulations since the conventional ana-
lytic treatment of cosmic density fluctuations via the hydrodynamical equations runs into severe problems even in a mildly non-linear regime. I will give an overview of Kinetic Field Theory, a novel analytic approach to cosmic large-scale structure formation, which provides a density fluctuation power spectrum that agrees well with state of the art N-body simulations up to k = 10h Mpc−1. I will point out how Kinetic Field Theory avoids the difficulties of standard perturbation theory by construction and allows to proceed deeply into the non-linear regime of density fluctuations. I will give a summary of the most important results and recent developments for cosmic structure formation and briefly show applications of Kinetic Field Theory outside of cosmology, stressing the opportunities this method provides for the study of the physics behind structure formation. I will then focus my discussion on how the form of the interaction potential influences the formation of cosmic structures in the highly non-linear regime and the implications it bears on the NFW density profile of dark matter halos.