Faculty of Mathematics
room 310, building E 2 4
mail: weber [at] math.uni-sb.de
office hours: by arrangement
Secretary: Laura Alin Schmigiel
room 108, phone +49-681-302-4432
My research is on compact quantum groups. I am working at the intersection of analysis, algebra and combinatorics, with links to free probability. Amongst others, I am primarily interested in symmetry structures within any framework, in particular a noncommutative one, i.e. structures involving noncommutative algebras arising in the context of operators on Hilbert spaces, matrices in linear algebra or observables in quantum physics, just to name a few. I am investigating compact quantum groups from different perspectives, using various methods interfering with many other areas of mathematics such as:
- Functional analysis: (universal) C*-algebras, von Neumann algebras, K-Theory
- Algebra: Hopf algebras, automorphisms of graphs, computer algebra
- Combinatorics: partitions of sets, finite graphs, counting problems
- Topology, cohomology: noncommutative topology (C*-algebras), K-Theory, (Hochschild) cohomology
- Quantum symmetries: "easy" quantum groups, noncommutative harmonic analysis, quantum automorphisms of graphs
- Geometry: noncommutative geometry, notions of symmetry, deformation/quantization
- Tensor categories: representation theory of quantum groups, Schur-Weyl results
- Quantum information theory: graph isomorphism games, construction of highly entangled quantum states
- Stochastical methods: distributional symmetries, free probability, Lévy processes
My main expertise is around "easy" quantum groups and the strategy to express analytic, algebraic or representation theoretical properties by purely combinatorial means.
What actually is Quantum Symmetry (Oberwolfach Snapshot)?
- Member of the Heisenberg programme of the German Research Foundation since April 2020. Heisenberg professor since March 2021.
- Principal Investigator in the SFB-TRR 195 Symbolic Tools in Mathematics and their Applications with the project Quantum Symmetries and Quantum Isomorphisms of Graphs, one PhD position, 2021-2024.
- Principal Investigator in the OPUS-LAP project quantum groups, graphs and symmetries via representation theory jointly funded by NCN and DFG, together with the Co-PI Adam Skalski, 2021-2023.
- von Kaven Ehrenpreis awarded by the German Research Foundation in 2021.
- Member of the Heisenberg programme of the German Research Foundation since April 2020.
- Invitation to the New Years Reception of the Federal President of Germany and Mrs Büdenbender, 10 January 2019 in the castle Bellevue, Berlin.
- Landespreis Hochschullehre 2016 (federal state teaching award) awarded by the first minister of Saarland for the Preparatory math courses for refugees for studies in MINT subjects See also the radio interview (in German) and the article in the online magazine of Saarland University.
- Best teaching award (faculty of mathematics) in summer term 2015, for the lecture on (Real) Analysis I
- Honorary Research Associate of Glasgow University, UK, 2015
- Best teaching award (faculty of mathematics) in winter term 2013/2014, for the lecture on functional analysis
- Oberwolfach Leibniz Graduate Student for the workshops C*-Algebras (2010) andC*-Algebras, Dynamics, and Classification (2012)
- scholarship by the Graduiertenkolleg Analytische Topologie und Metageometrie from 2008 until 2010
- scholarship by the Studienstiftung des deutschen Volkes from 2002 until 2006
Since 1 January 2017, I am one of the PI's of the SFB-TRR 195 Symbolic Tools in Mathematics and their Applications (RWTH Aachen, TU Kaiserslautern, Saarland University, and others), funded by the DFG (German Research Foundation).
My project in the first phase (2017-2020) was: I.13 - Computational classification of orthogonal quantum groups.
My project in the second phase (2021-2024) is: A25 - Quantum symmetries and quantum isomorphisms of graphs
Audit Chair of the study program VSi MINT
Audit Chair of the study program BSc/MSc Mathematics and Computer Science
Department of Mathematics
Postfach 15 11 50
Campus building E 2 4