Vertex algebras and factorization algebras are two approaches to chiral conformal field theory, a part of quantum field theory related to holomorphic functions of a single variable. Many examples of chiral CFT's have been constructed as vertex algebras. Factorization algebras as studied by Costello and Gwilliam are a relatively new approach to quantum field theory which applies to all kinds of geometries, including higher-dimensional ones. We focus on ℂ, the plane of complex numbers.

Some examples of chiral CFT's have already been constructed as factorization algebras but not all of them. Furthermore, Costello and Gwilliam show how every suitable factorization algebra on ℂ gives rise to a vertex algebra. In my thesis, I show that every vertex algebra arises from a factorization algebra.

I have split my thesis into two articles:
Let me know if you have comments or questions. **Email:** danielbruegmann[at]mpim-bonn[dot]mpg[dot]de
## Teaching

I was a teaching assistant at the University of Bonn for four semesters.
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Academic visits

My advisors are Peter Teichner and André Henriques. My research has been generously funded by the Max Planck Institute for Mathematics in Bonn.

- Winter 2018/2019: Algebraic Topology 1 (Martin Palmer)
- Summer 2016: Topology 2 (Viktoriya Ozornova)
- Winter 2015/2016: Topology 1 (Peter Teichner)
- Winter 2011/2012: Analysis 1 (Matthias Lesch)

- 2019: Visitor at the Maths Institute in Oxford for four weeks
- January – June 2017: Visiting Student Researcher at UC Berkeley
- September – December 2016: Recognised Student at Oxford
- January – June 2014: Visiting Student Researcher at UC Berkeley