# Lucas Mann receives the Hausdorff Memorial Award

## PhD student of Peter Scholze proves a Poincaré duality in the case of p-adic geometry

**Bonn, 18.01.2023. The Department of Mathematics (Fachgruppe Mathematik) honors Lucas Mann for the best dissertation of the academic year 2021/2022 in mathematics with the Hausdorff Memorial Prize. The honor today was presented by the chair of the Department, Anton Bovier, between the two lectures of the Hausdorff Colloquium in the Lipschitz Hall.**

Lucas Mann's PhD thesis deals with a fundamental property of compact manifolds, called Poincaré duality, and attempts to apply it to p-adic geometry. In algebraic topology, the Poincaré duality theorem is an important result and makes a statement about the isomorphism between groups of cohomology and homology of an orientable manifold. The aim of the thesis supervised by Peter Scholze was to formulate and prove this Poincaré duality theorem in a meaningful way for certain spaces over fields of mixed characteristic with arbitrary coefficients. Starting from this aim, however, Lucas Mann developed much more, namely a complete theory on almost 300 pages, from which the desired Poincaré duality theorem then follows naturally, quasi as a by-product. Lucas Mann uses the whole range of technically highly sophisticated, latest state-of-the-art mathematical developments, such as higher topos theory, perfectoid spaces and condensed mathematics. In addition, concepts that are intuitively difficult to access are introduced and motivated with great didactic skill. The thesis impresses with elegance and clarity. Peter Scholze is highly impressed by the technical level and the importance of the theses beyond the statement to be proved: "This PhD thesis is an extraordinary contribution to p-adic geometry, and it will take some years to digest the statements from this thesis."

The Hausdorff Memorial Prize is awarded in honor of Felix Hausdorff each year around the anniversary of his death, January 26, at the Hausdorff Colloquium. The professors and lecturers have the right to nominate candidates. The decision is made by a jury appointed by the Department of Mathematics. The prize consists of 500 euros in prize money and a book prize.