The MaPS seminar is a hybrid event; held from 16.00 - 17.00 hrs in room ZI-4070 and via TEAMS.
Feel free to reach out if you want to present your work in an upcoming session!
Send us an email!
The MaPhS organizers,
Maike de Jongh, Lars Schroeder and Alexander Wierzba
upcoming dates:
2025:
- 04-06-2025
Speaker: Jens de Vries
Title: Spectral constants via contour integral methods
Abstract: When applying a function to a matrix --- say, the exponential or a rational function --- one often asks how the norm of the resulting matrix compares to the norm of the function itself. This question leads to the concept of c-spectral sets, which captures how well the supremum norm of a function on a set in the complex plane controls the operator norm of the matrix. A central open problem in this area is Crouzeix's conjecture, which asserts that the numerical range of any matrix is a c-spectral set with spectral constant c=2. A key tool in this context is the double-layer potential --- an integral kernel on the boundary of a domain whose integral operators have delicate boundary behavior. In this talk, I will discuss how these integral operators can be used to characterize the hypotheses appearing in this conjecture and how they lead to spectral constants for the numerical range. This talk is based on joint work with Felix Schwenninger.