Meike Neuwohner addresses in her PhD thesis "Improved Approximation Algorithms for Weighted k-Set Packing", supervised by Stefan Hougardy, approximation algorithms for the k-set packing problem, a fundamental question in combinatorial optimization. The results include the first improvement in the approximability of the problem in over twenty years. The first set of results not only strengthened the previous local search techniques, but also showed that a new algorithm in the thesis gives the asymptotically best achievable bound using local improvements. Overall, the results significantly improve our understanding of a fundamental problem, by developing new techniques and insights, while also charting their limitations. The results of the thesis were published in prestigious conferences and journals, including SODA 2023, IPCO 2022, and Mathematical Programming. The presentation of the results is also excellent: all reviewers praised the clear structure, rigour and clarity, as well as the intuitions provided in the exposition of complex technical arguments.
In his PhD thesis "The Sup-Norm Problem For Automorphic Forms In Higher Rank", supervised by Valentin Blomer, Radu Toma deals with sup-norm estimates of automorphic forms on groups of higher rank. Automorphic forms are an interface between various mathematical topics: from an analytical perspective, they are eigenfunctions of Laplace operators on symmetric spaces, from the perspective of representation theory, they are elements of irreducible representations. They contain information about properties of arithmetic objects in number theory. Since 1995, initiated by a paper by Iwaniec and Sarnak in the Annals of Mathematics, these estimates have received the greatest attention. Radu Toma was the first to show uniform estimates in the covolume and in the spectral parameter, both in the cocompact and non-cocompact case. The result in the cocompact case has already been well published. The non-cocompact case is much more difficult and all eviewers are impressed and surprised by this.
The Hausdorff Memorial Prize is awarded in honor of Felix Hausdorff every year around the anniversary of his death, January 26, as part of the Hausdorff Colloquium. Professors and private lecturers have the right to nominate candidates. The decision is made by a jury appointed by the Department of Mathematics. The award consists of prize money of 500 euros and a book prize. This year, the prize money was split.