I am a PhD student at the Department of Mathematical Sciences, Chalmers University of Technology/University of Gothenburg. My main supervisor is Julie Rowlett.
I graduated MScEng (civilingenjör) at Chalmers in 2023. In my Master's thesis I studied the heat trace expansion of domains in the Euclidean plane.
Research interests
Spectral theory
Differential geometry
Number theory
Current position
PhD student in mathematics at Chalmers/GU
Main supervisor: Julie Rowlett
Co-supervisor: Simon Larson
Hobbies
Table tennis
Reading
Physical endurance
Popular Science Research Overview
Spectral theory is a branch of mathematics that studies the spectrum of operators. An operator can be thought of as a mathematical rule that transforms one function into another. Certain operators arise naturally when describing physical processes, and one of the most important of these is the Laplace operator. The Laplace operator appears in several fundamental equations in physics. For example, the heat equation describes how heat spreads through a material over time, the wave equation models vibrations such as sound or waves on a string, and the Schrödinger equation is central in quantum mechanics and describes how quantum systems evolve. Because these equations involve the Laplace operator, understanding the behavior of this operator is essential for understanding the physical phenomena they describe.
One of the most powerful ways to study an operator is through its eigenvalues, which together form its spectrum. Eigenvalues reveal intrinsic properties of the system. In Swedish, eigenvalues are called egenvärden, where egen relates to egenskap, meaning a characteristic or property. This reflects the mathematical idea: eigenvalues capture fundamental features of the operator and the processes it describes.
The spectrum can reveal a lot of information about the system, but it does not determine everything. Different systems can sometimes share exactly the same spectrum, a phenomenon known as isospectrality. This leads to deep and interesting questions. For example, if two geometric shapes have the same spectrum for their Laplace operator, how similar are they really?
My research lies at the intersection of spectral theory and geometry. I study how geometric properties of spaces, such as their shape or structure, affect the spectrum of operators defined on them. In particular, I investigate cases where different geometries produce the same spectrum, helping us understand both what spectral data can reveal about a space and what information it leaves hidden.
Education and Theses
Bachelor's degree 2018-2021: Engineering Mathematics at Chalmers University of Technology. Bachelor's thesis: Fourierserieutveckling av andra ordningens Eisensteinserier, with Albin Ahlbäck, Erik Bivrin and Victor Brun (2021).
Master's degree 2021-2023: Engineering Mathematics and Computational Science at Chalmers University of Technology. Master's thesis: The mathematics of hearing the shape of a drum and filling Kac's holes (2023).
Licentiate thesis: Geometric Spectral Invariants and Isospectrality (2025).
Teaching Experience
I have been a teaching assistant for a total of 12 undergraduate mathematics courses at Chalmers/GU, many of which I have taught several times. Topics include single and multivariable calculus, linear algebra, probability and statistics, and Fourier analysis. Some of them also contained computational parts. In some of the courses, I have also helped to design and correct exams.
Mentor på Sommarmatten, Chalmers University of Technology, 2022-2023.
Examiner for part of L3MA11: Mathematics for teachers grade 1-3, University of Gothenburg, 2024.
Supervision
Bachelor's thesis at Chalmers about flat tori, spring 2024. Students: Filippa Hultin, Madicken Astorsdotter, and William Karlsson. Thesis: Jakten på fyrdimensionella tripletter av isospektrala, icke-isometriska platta torusar.