13 February 2025

Photo: Kristoffer Rasmussen

In the summer of 2022, Kristoffer Rasmussen graduated from the University of Copenhagen, which is also his hometown, with a master's degree in mathematics specializing in algebraic topology and category theory. For his master's thesis, he worked on "One-dimensional factorization homology and string-nets". He joined the Mathematics Department at the University of Hamburg for his PhD studies under the supervision of Dr. Julian Holstein.

What is the topic of your research?

Working in the Algebra and Number Theory group, I focus on derived categories of the second kind, global Koszul duality, and Hochschild cohomology. In the last year, I have studied the compactly generated derived category associated to a dg-algebra. Specifically looking for a class of dg-algebras for which we can give an explicit description of the compact generators. Gaining a deeper understanding of these compact generators will help us compute the Hochschild cohoology of the compactly generated derived category. 

What fascinates you about your research focus?

I have been mesmerized by homological algebra ever since I was first introduced to the field in my bachelor's program. It is a rich theory that supplies tools for various branches of mathematics and theoretical physics. The theory of derived categories of the second kind was developed because classical homological algebra was found inadequate in studying Koszul duality. 

What do you like about Quantum Universe?

I enjoy the QU Days as they offer a chance to meet other PhD students with diverse backgrounds. As a mathematician with limited knowledge of physics, I see these events as opportunities to learn about physics and what fascinates physicists. QURS has many useful and relevant soft skills courses, which I plan to take advantage of in the future. 

What do you like to do in your free time?

I spend most of my time practicing German. I also enjoy exploring the city's events and the music scene. I am hoping to soon experience it all in German!