Fakultätspreisträger Fachbereich Mathematik, Statistik und Informatik

Laudatio

In his master's thesis «The essential numerical range of type 5», which was awarded the highest degree 6.0, Nicolas Hefti achieved a truly remarkable result with highly unexpected methods. He solved a hard open problem for unbounded linear operators in infinite dimensional Hilbert spaces. Unexpectedly, his proof uses an abstract result for Banach spaces which have less structure than Hilbert spaces.

Moreover, he succeeded to generalize a geometric property of essential numerical ranges, making nume-rous earlier results special cases of his result. In view of applications, the abstract results of his thesis have implications to capture and detect the unwanted phenomenon of spectral pollution where numerical approximations of eigenvalues converge to limits that are no true eigenvalues (spurious eigenvalues).

The outstanding master's thesis of N. Hefti has already become the basis of a scientific paper that will soon be submitted (and will already be his second publication).

Laudatio

The collection of total orders on a group corresponds both to a topological space and to a class of algebraic structures. In her PhD thesis “Order, Algebra, and Structure: Lattice-Ordered Groups and Beyond”, Dr. Almudena Colacito shows that total orders on groups can also be understood as equations, and that descriptions of total orders can be understood as proofs of those equations. Moreover, she shows that the total orders on an already partially ordered group correspond to the spectral space of a certain free algebra. She then uses these remarkable and unexpected bridges between the proof theory, algebra, and topology of ordered groups to develop new structure theory for ordered algebraic structures and to obtain new algorithms for deciding properties in algebra and logic.