Seminar

The workgroup's seminar GOAT (Gruppen- und Operatoralgebren-Treffen) currently takes place Wednesdays 10:15 - 11:45 in room 0.14 of house 9 on campus Golm unless specified differently.

Winter 2024/25

• 30.10.2024
  Sven Raum (University of Potsdam)
  K-theory of Hecke C*-algebras

  Hecke C*-algebras are deformations of the group C*-algebra of Coxeter groups. Their K-theory could so far only be determined in few cases. I will survey these and provide ideas of proof for the case of right-angled Hecke C*-algebras, whose K-theory we computed in joint work with Adam Skalski. This result has applications in the classification of Hecke C*-algebras.

• 23.10.2024
  Jamie Bell (University of Münster)
  An invitation to stable rank for C*-algebras

  Thanks to Gelfand duality, C*-algebras are often considered noncommutative topological spaces. A very profitable approach to studying C*-algebras is to formulate noncommutative generalisations of classical topological notions. This philosophy leads, for instance, to the noncommutative geometry programme and operator K-theory.

  For C*-algebras, the concept of Lebesgue covering dimension stratifies into many different notions; in any case, a low noncommutative dimension is considered an important regularity property for C*-algebras. The need for such notions is brought into sharp focus by the success of the Elliott classification programme for classifying simple, separable and nuclear C*-algebras, where finite nuclear dimension (equivalently, 𝒵-stability) is -- modulo the UCT, which may be automatic for nuclear C*-algebras -- the linchpin required to obtain a complete classification theorem.

  In the early 80s, Marc Rieffel introduced the first noncommutative generalisation of covering dimension, stable rank, to answer questions related to non-stable K-theory. In the intervening years, C*-algebras with stable rank one have emerged as a rich class with many desirable properties. In this talk, we introduce stable rank for C*-algebras and discuss examples of C*-algebras having low stable rank, particularly those arising from groups and dynamical systems. This is complemented by a survey of some applications of stable rank one. Time permitting, we discuss some open problems and mention approaches to generalise stable rank one results to crossed products arising from non-amenable topological dynamical systems. This is joint work in progress with Shirly Geffen, Sven Raum and Jonathan Taylor.

• 16.10.2024
  Jonathan Taylor (University of Potsdam)
  Two groupoid C*-algebra constructions with the same name that we're not actually sure whether they're the same or not

  Since Renault's reconstruction of Cartan pairs as (twisted) groupoid C*-algebras, later generalisations of the theory have partially diverged. Staying in the realm of C*-algebras with a 'large' commutative subalgebra, there are (at least) two generalisations: weak Cartan pairs and essential Cartan pairs. Both of these definitions then admit reconstruction theorems utilising competing definitions of an "essential groupoid C*-algebra", and it is currently not known whether these two definitions differ.

  In talk I will describe the similarities and differences between these two definitions of essential groupoid C*-algebras, and the approaches and techniques of which they make use.

Summer 2024

• 03.07.2024 at 10:15 - 11:45
  Jonathan Taylor (University of Potsdam)
  Functoriality for groupoid C*-algebras

  Groupoid homomorphisms do not, generally, lift (functorially) to *-homomorphisms of the associated C*-algebras. The crux of this lies in the fact groupoids span a class of objects ranging from groups to topological spaces, and the C*-algebra construction is covariantly functorial for groups and their homomorphisms, but contravariantly functorial for spaces and their continuous maps.

  Actors form an alternative morphism between groupoids which induce *-homomorphisms between C*-algebras while encompassing both group homomorphisms and (opposite) continuous maps. A natural question following this is, under what conditions is a *-homomorphism between groupoid C*-algebras induced by an actor of the underlying groupoids? In this talk I will provide a partial answer, showing a reconstruction of groupoid actors between effective groupoids from *-homomorphisms preserving certain (Cartan) structure of the C*-algebras.

• 26.06.2024 at 10:15 - 11:45
  Hang Wang (East China Normal University)
  Higher Kazhdan projections and delocalised ℓ²-Betti numbers

  We introduce the K-theory class of higher Kazhdan projections and its relation with a variant of Lott's delocalised ℓ²-Betti numbers. We will also relate the K-theory class of higher Kazhdan projections with the Euler class under the Baum-Connes assembly map over a small class of examples. This is joint work with Sanaz Pooya.

• 05.06.2024 at 10:15 - 11:45
  Wushi Goldring (Stockholm University)
  Propagating the algebraicity of automorphic representations via functoriality

  My talk concerns the algebraic properties of automorphic representations. These infinite-dimensional representations of reductive groups over number fields are defined using harmonic analysis. For every prime p, they admit p-adic analogues of Laplacian eigenvalues called Hecke eigenvalues. One of the main mysteries of the Langlands Program is that some automorphic representations have algebraic Hecke eigenvalues while others have transcendental ones. For some, the algebraicity follows from the geometry of Shimura varieties and/or locally symmetric spaces, while for others there are conjectures predicting either algebraicity or transcendence. But there are also instances where it is unclear whether to expect algebraic or transcendental eigenvalues.

  I will discuss when Langlands Functoriality, another central theme of the Langlands Program, can be used to reduce the algebraicity for a representation π of a group G to that of some other representation π' of some other group G' for which algebraicity is known for geometric reasons. Via difficult dictionaries, this translates into much more elementary problems in group theory. In the negative direction, we give several group-theoretic obstructions to the existence of π'. In particular, this gives a conceptual explanation for why π' doesn't exist when π arises from non-holomorphic analogues of modular forms called Maass forms. In the positive direction, we exhibit new cases of algebraicity of Hecke eigenvalues for automorphic representations for which no direct link to geometry is known. For some of these, we also associate the Galois representations predicted by the Langlands correspondence.

• 22.05.2024 at 10:15 - 11:45
  Ada Masters (University of Wollongong)
  Spectral triples for group C*-algebras from geometric group theory

  Since Connes’s 1989 paper, the use of length functions to build spectral triples for group C*-algebras has become commonplace in noncommutative geometry. This construction, although sound at the level of quantum metric spaces, always gives rise to trivial K-homology. Using ingredients from geometric group theory, this can be remedied for many CAT(0) groups, including non-discrete groups. In the process, a novel group invariant from (quantum-group-equivariant) KK-theory is uncovered. The understanding of group extensions in this framework is a microcosm of the more general problem of the constructive unbounded Kasparov product. I will also touch on the problem of building spectral triples for crossed product C*-algebras arising from dynamical systems, using the Kasparov product and new tools inspired by conformal geometry.

• 10.05.2024 at 14:15 - 15:15 in room 2.09.2.22. This is a Friday.
  Adam Rennie (University of Wollongong)
  The Levi-Civita connection on noncommutative differential forms.

  I will discuss the main results and consequences of recent work with Bram Mesland. Using mostly algebraic techniques, with just a little Hilbert module analysis, we present necessary and sufficient conditions for the existence of Hermitian torsion-free connections on noncommutative one-forms, such as those arising from spectral triples. Various consequences and examples will be discussed also.

• 26.04.2024 at 15:00 - 16:00 in room 2.09.0.14
  Christian Lomp (University of Porto)
  Properties of affine cellular algebras

  Motivated by Lusztig's basis of Hecke algebras, Graham and Lehrer introduced cellular algebras in 1996. As a generalisation of Graham and Lehrer’s cellular algebras, affine cellular algebras have been introduced by Koenig and Xi in order to treat affine versions of diagram algebras like affine Hecke algebras of type A and affine Temperley–Lieb algebras in a unifying fashion. Since then several classes of algebras, like the Khovanov-Lauda- Rouquier algebras or Kleshchev’s graded quasihereditary algebras have been shown to be affine cellular.

  Roughly speaking, an affine cell ideal of an algebra A with involution * is a *-ideal J that is isomorphic as an A-bimodule to a generalized matrix ring M_n(B) over some commutative affine k-algebra B, whose multiplication is deformed by some "sandwich" matrix ψ, i.e. the product of two matrices x and y is defined to be x ψ y. An affine cellular algebra is then in particular a *-algebra A that admits a chain of *-ideals J₀ < J₁ < J₂ < … < J_n =A such that each quotient J_i/J_i-1 is an affine cell ideal of A/J_i-1. In this talk I will exhibit some ring theoretical properties of affine cellular algebras. In particular we will show that any affine cellular algebra A satisfies a polynomial identity. Furthermore, we show that A can be embedded into its asymptotic algebra if the occurring commutative affine k-algebras B_j are reduced and the determinants of the "sandwich" matrices are non-zero divisors. As a consequence we show that the Gelfand- Kirillov dimension of A (which measures the growth of the algebra) is less or equal to the largest Krull dimension of the algebras B_j and that equality holds in case all affine cell ideals are finitely generated (e.g. idempotent) or if the Krull dimension of the algebras B_j is less or equal to 1. Special emphasis is given to the question when an affine cell ideal is idempotent, generated by an idempotent or finitely generated.

  This is joined work with Paula Carvalho, Steffen Koenig and Armin Shalile

• 17.04.2024 at 10:15 - 11:45
  Ulrik Enstad (University of Oslo)
  Duality principles for frames and Riesz sequences via Morita equivalence

  Frames provide a robust notion of infinite spanning sequences in a Hilbert space. Dually, a Riesz sequence is a strong type of linearly independent sequence. The frame property of certain structured function systems is sometimes equivalent to the Riesz sequence property of an associated function system. There are several such so-called duality principles in applied harmonic analysis, and I aim to convey in this talk that they can all be unified by a more abstract duality principle for Morita equivalence bimodules. This is joint work with Franz Luef.

• 10.04.2024 at 10:15 - 11:45
  Anatolii Zhuchok (Luhansk Taras Shevchenko National University, Poltava)
  Relatively free trioids

  A trioid is an algebraic system consisting of a set with three binary associative operations satisfying certain axioms. Trioids are a generalization of semigroups. They play a prominent role in trialgebra theory. After defining the concept of a trioid we present examples of trioids and their relationships with such algebraic structures as Poisson algebras, Leibniz algebras, dialgebras, dimonoids, digroups and n-tuple semigroups. Then we establish independence of axioms of trioids and construct absolutely and relatively free algebras in trioid variety.

Winter 2023/2024

• 08.02.2024 at 10:15 - 11:45 (room 5.05 of house 5)
  Tristan Bice (Czech Academy of Sciences)
  Cartan Semigroups

  Cartan subalgebras allow C*-algebras to be represented on effective twisted étale groupoids by utilising key properties of their normaliser semigroup. Isolating these key properties, we formulate an appropriate notion of "Cartan semigroup" that allows us to represent C*-algebras on even non-effective groupoids. To each such semigroup there is again a corresponding commutative "semi-Cartan subalgebra" although it may no longer be maximal commutative and, moreover, a single semi-Cartan subalgebra may arise from various different Cartan semigroups, which yield different groupoid representations. In this talk we will outline this generalised Weyl groupoid construction and compare it to some general Fell bundle representations previously investigated by the speaker.

  This is work in progress with Jonathan H. Brown, Lisa Orloff-Clark, Ying-Fen Lin and Kathryn McCormick.

• 07.02.2024 at 10:15 - 11:45 (room 0.12 of house 9)
  Hannes Thiel (Chalmers)
  Semiprimitive ideals in C*-algebras

  Nonclosed ideals of bounded operators play a prominent role in the theory of singular traces as developed by Dixmier, Connes and many others, and the Calkin correspondence is a powerful tool that can be used to answer many questions about nonclosed ideals in this context. For general C*-algebras, a systematic study of nonclosed ideals was initiated by Pedersen in the late 1960s, but much less is known in this broader setting.

  We show that a not necessarily closed ideal in a C*-algebra is semiprime (that is, an intersection of prime ideals) if and only if it is closed under roots of positive elements. Quite unexpectedly, it follows that prime and semiprime ideals in C*-algebras are automatically self-adjoint. This can be viewed as a generalization of the well-known result that closed ideals in C*-algebras are semiprime and self-adjoint.

  This is joint work with Eusebio Gardella and Kan Kitamura.

• 16.11.2023 at 10:15 - 11:45 (online, please contact me for login data)
  Jianchao Wu (Fudan University)
  Long thin covers and finite nuclear dimension for crossed product C*-algebras

  Finite nuclear dimension is a regularity property of C*-algebras that have played a pivotal role in the Elliott classification program of C*-algebras. It has been a key problem in the field to verify this property for crossed product C*-algebras associated to topological and C*-dynamical systems. Previous results have mainly focused on the case of free actions. In a recent preprint (joint with Hirshberg), we show that any topological action by a finitely generated virtually nilpotent group on a finite-dimensional space gives rise to a crossed product with finite nuclear dimension. This is shown by introducing a new topological-dynamical dimension concept called the long thin covering dimension. This result can be strengthened further and applied to some allosteric (and thus non-almost-finite) actions by certain wreath product groups. Another application yields the result (joint with Eckhardt) that (twisted) group C*-algebras of virtually polycyclic groups have finite nuclear dimension.

• 02.11.2023 at 10:15 - 11:45
  Adam Dor-On (Haifa University)
  Ratio-limits and Toeplitz quotients for random walks on relatively hyperbolic groups

  When studying quotients of C*-algebras generated by creation and annihilation operators on analogues of Fock space, the existence of a unique smallest equivariant quotient becomes an important question in the theory. When it exists, this quotient is sometimes called the co-universal quotient. The study goes back to uniqueness theorems of Cuntz, and Cuntz and Krieger, which were extended by many authors to include several broad classes of examples.

  When associating Toeplitz C*-algebras to random walks, new notions of ratio-limit space and ratio-limit boundary emerge from computing natural quotients, and the question of co-universality becomes intimately related to the geometry and the dynamics on the boundary of the random walk.

  In this talk I will explain how we extended results of Woess and myself to show that there is a co-universal quotient for a large class of symmetric random walks on relatively hyperbolic groups. This allowed us to make significant progress on some questions of Woess on ratio-limits for random walks on relatively hyperbolic groups, and shed light on the general question of co-universality for Toeplitz C*-algebras arising from subproduct systems.

  This talk is based on joint work with Matthieu Dussaule and Ilya Gekhtman.

• 24.10.2023 at 11:00 - 12:00 in room 1.22 of house 9 on campus Golm
  André Nies (University of Auckland)
  Totally disconnected locally compact groups, groupoids, and computability

  We introduce t.d.l.c. groups and then study their algorithmic aspects. A useful tool is the meet groupoid, which is the natural groupoid on compact open cosets, enriched by the intersection operation. Joint work with A. Melnikov.

• 19.10.2023 at 10:15 - 11:45
  Jonathan Taylor (University of Potsdam)
  Essential Cartan pairs and their non-Hausdorff groupoid models

  Renault's theorem for Cartan pairs of C*-algebras states that C*-algebras with particularly nice commutative subalgebras, called Cartan subalgebras, admit twisted groupoid models. One of the conditions that Renault required of a Cartan subalgebra was that there is a conditional expectation projecting from the ambient C*-algebra down to the subalgebra. In the groupoid setting, this corresponds to restricting functions on the groupoid to the unit space of the groupoid. In my PhD thesis, I showed that this condition can be relaxed, to allow for algebras that do not project nicely down to the subalgebra, but have conditional expectations taking values in a slightly larger algebra. Such inclusions still have twisted groupoid models, but the groupoids are no longer Hausdorff.

Summer 2023

• 18.07.2023 (this is a Friday) at 09:00 - 10:30 in room 2.22
  Georg Lehner (FU Berlin)
  The Rosenberg Conjecture through the lens of Solidification

  The Rosenberg Conjecture states that for a given Banach Algebra A, the comparison map between algebraic and topological K-theory becomes an isomorphism on finite coefficients. The new framework of condensed mathematics developed by Scholze et.al. allows one to frame this question in a different way. Condensed sets are a replacement for topological spaces that work well in their interplay with algebraic constructions. In particular, if we view our Banach algebra A as a condensed ring, we can equip the algebraic K-theory groups of A with the structure of condensed abelian groups. There exists a natural notion of completion for condensed abelian groups called solidification. The map from the K-theory of A into its solidification recovers the comparion map from algebraic to topological K-theory, allowing one to phrase the Rosenberg conjecture as a topological statement about the condensed structure of the K-theory of A.

• 06.07.2023
  Dan Ursu (University of Münster)
  Simplicity of crossed products by FC-hypercentral groups

  Results from a few years ago of Kennedy and Schafhauser characterize simplicity of reduced crossed products AxG, where A is a unital C*-algebra and G is a discrete group, under an assumption which they call vanishing obstruction. However, this is a strong condition that often fails, even in cases of A being finite-dimensional and G being finite.

  In joint work with Shirly Geffen, we find the correct two-way characterization of when the crossed product is simple, in the case of G being an FC-hypercentral group. This is a large class of amenable groups that, in the finitely-generated setting, is known to coincide with the set of groups which have polynomial growth. With some additional effort, we can characterize the intersection property for AxG in the non-minimal setting, for the slightly less general class of FC-groups. Finally, for minimal actions of arbitrary discrete groups on unital C*-algebras, we are able to generalize a result by Hamana for finite groups, and characterize when the crossed product AxG is prime.

  All of our characterizations are initially given in terms of the dynamics of G on I(A), the injective envelope of A. This gives the most elegant characterization from a theory perspective, but I(A) is in general a very mysterious object that is hard to explicitly describe. If A is separable, our characterizations are shown to be equivalent to an intrinsic condition on the dynamics of G on A itself.

• 22.06.2023
  Ulrik Enstad (University of Potsdam)
  Linear independence of coherent systems associated to discrete subgroups

  The HRT conjecture states that any finite set of time-frequency shifts of a nonzero, square-integrable function is linearly independent. While the conjecture is still open, it was settled by Linnell in the case where the time-frequency shifts belong to a discrete subgroup of R^d. In this talk I will present an elementary proof of Linnell's theorem which also extends to other settings, in particular to any coherent system arising from a projective discrete series of a simply connected, nilpotent Lie group.
  The talk is based on recent joint work with Jordy Timo van Velthoven.

• 15.06.2023
  David Kerr (University of Münster)
  Entropy, orbit equivalence, and the Rokhlin lemma

  I will discuss some recents applications and developments surrounding the Ornstein-Weiss Rokhlin lemma involving quantitative versions of orbit equivalence and questions of tileability in topological dynamics.

• 08.06.2023
  Fernando Lledo (University Carlos III de Madrid)
  The dichotomy amenable/paradoxical in inverse semigroups and their uniform Roe algebras.

  In the present talk I will briefly review certain aspects of the dichotomy amenable/paradoxical in the category of metric spaces and inverse semigroups. Then I will address the question of defining a reasonable metric structure on a discrete inverse semigroup and study the properties of its uniform Roe algebra like Foelner type conditions, nuclearity or exactness.

  [1] F. Lledó and D. Martínez, The uniform Roe algebra of an inverse semigroup, Journal of Mathematical Analysis and Applications 499 (2021) 124996.
  [2] P. Ara, F. Lledó and D. Martínez, Amenability and paradoxicality in semigroups and C*-algebras, Journal of Functional Analysis 279 (2020) 10853.
• 25.05.2023
  Maria Gerasimova (University of Münster)
  A family of exotic group C*-algebras coming from piecewise -projective groups

  An exotic group C*-algebra of a group G is a C*-algebra that lies naturally in between the reduced and the universal group C*-algebra of G. The existence of an exotic C*-algebra can be viewed in some sense as a refinement of the non-amenability of G. We will discuss several approaches to construct such algebras and then will describe the explicit construction of a family of exotic group C*-algebras coming from the family of piecewise-projective groups. This is a joint work with Nicolas Monod.

• 27.04.2023
  Federico Vigolo (University of Göttingen)
  An invitation to coarse groups

  Coarse groups are spaces equipped with operations that satisfy the group axioms up to uniformly bounded error. The study of coarse groups, actions and homomorphisms was only very recently initiated and leads to a number of questions and research directions. This talk is an introduction to the subject (joint work with Arielle Leitner).

• 17.04.2023 (this is a Monday) at 13:00 in room 1.10
  Emilie Elkiær (University of Oslo)
  On the L^p-representation theory of virtually abelian compact groups

  The virtually abelian locally compact groups were characterized in representation theoretic terms by C. Moore in the 70s as those groups for which there is a uniform bound on the degree of their irreducible representations. For compact groups, this, in turn, provides a uniform bound on the norm of a certain family of projections appearing in their L^p-representation theory. We shall discuss to what extent this characterizes the virtually abelian groups among the compacts.

• 13.04.2023
  Eduard Vilalta (Universitat Autònoma de Barcelona)
  Divisibility properties for Cuntz semigroups

  Divisibility properties for Cuntz semigroups play an important role in the study of both simple and non-simple C*-algebras. The prime example of this is the remaining open implication of the Toms-Winter conjecture which, under the assumption of locally finite nuclear dimension, boils down to studying if strict comparison implies almost divisibility. In this talk I will recall what these divisibility properties are, focusing specifically on those introduced by Robert and Rørdam. I will discuss how these notions give rise to natural classes of C*-algebras, and explain their connection to non-simple analogues of the Toms-Winter conjecture. I will also talk about the Global Glimm Problem, which predicts that two of these properties are equivalent. The talk is based on joint work with Hannes Thiel.

• 19.01.2023
  Rachel Skipper (ENS Paris)
  Finiteness properties for simple groups

Autumn 2022

• 13.12.2022
  David Kyed (University of Southern Denmark)
  Symmetrized noncommutative tori and their classification
• 03.11.2022
  Sayan Chakraborty (ISI Calcutta)
  Symmetrized noncommutative tori and their classification
• 12.09.2022
  Hannes Thiel (CAU Kiel)
  The zero-product structure of C*-algebras

Spring 2022

• 28.04.2022
  Mario Klisse (TU Delft)
  On the isomorphism class of q-Gaussian C*-algebras
• 10.03.2022
  Jordy van Velthoven (TU Delft)
  Density theorems for discrete series restricted to lattices

Wednesday Zoom Seminar

During the Corona pandemic, the Wednesday Zoom Seminar combined speakers in algebraic geometry, group theory and operator algebras.

All abstracts can be found in the SMC calender: Link.

HAOART Seminar

Due to the Corona pandemic, our seminar on Harmonic Analysis, Operator Algebras and Representation Theory (pronounced "Howard") is was suspended and eventually discontinued.

All abstracts can be found in the SMC calender: Link.

Spring 2020

• 04.03.2020
  Rolf Källström (Högskolan i Gävle)
  Decompositions of D-modules over finite maps and the correspondence with representations of finite groups
• 26.02.2020
  Michael Hartz (University of Hagen)
  Multipliers and operator space structure of weak products
• 05.02.2020
  Eskil Rydhe (Lund University)
  On Laplace-Carleson embeddings, and some aspects of the Fourier transform
  
• 29.01.2020
  Wushi Goldring (Stockholm University)
  Propagating algebraicity of automorphic representations via Langlands functoriality

Autumn 2019

• 04.12.2019
  Odysseas Bakas (Lund University)
  Remarks on a theorem of Pichorides
• 27.11.2019
  Christian Bönicke (University of Glasgow)
  Regularity properties for ample groupoids
• 13.11.2019
  Yash Lodah (EPFL)
  Finitely generated infinite simple groups of homeomorphisms of the real line
• 13.11.2019
  Asaf Horev (Stockholm University)
  Geometric representation theory and factorization homology on surfaces
  (Joint with the NT seminar at 11 o`clock, room 306)
• 30.10.2019
  Arno Kret (University of Amsterdam)
  Construction of Galois representations for GSO_2n
• 04.09.2019
  Ulrik Enstad (University of Oslo)
  Time-frequency analysis on the adeles

Spring 2019

• 29.05.2019
  Constanze Liaw (University of Delaware)
  Generalizations of Aleksandrov-Clark theory
• 22.05.2019
  David Kyed (University of Southern Denmark)
  Uniqueness questions for C*-norms on group rings
• 15.05.2019
  Alan Sola (University of Stockholm)
  The Dirichlet space of the bidisk: a survey
• 08.05.2019
  Nadia Larsen (University of Oslo)
  Phase transitions and arithmetic subalgebras for Hecke C*-algebras from number fields
• 24.04.2019
  Magnus Goffeng (University of Gothenburg/Chalmers)
  The dynamics and (noncommutative) geometry of Smale spaces

Publications

All my publications can be found on MathSciNet, zbMATH and ArXiv.

Preprints

• Free actions of polynomial growth Lie groups and classifiable C*-algebras
  with Ulrik Enstad and Gabriel Favre
  ArXiv (2023)

• Detecting ideals in reduced crossed product C*-algebras of topological dynamical systems
  with Are Austad
  ArXiv (2023)

• The ideal intersection property for essential groupoid C*-algebras
  with Matthew Kennedy, Se-Jin Kim, Xin Li and Dan Ursu
  ArXiv (2021)

Research articles

1. Twisted group C*-algebras of acylindrically hyperbolic groups have stable rank one
   Accepted for publication in Groups, Geom. and Dyn. ArXiv version (2024)

2. A dynamical approach to non-uniform density theorems for coherent systems
   with Ulrik Enstad
   Accepted for publication in Trans. AMS. ArXiv version (2022)

3. On the centre of Iwahori-Hecke algebras
   with Timothée Marquis
   J. Algebra 656 (2024), 276-293 and the ArXiv version

4. Factorial multiparameter Hecke von Neumann algebras and representations of groups acting on right-angled buildings
   with Adam Skalski
   J. Math. Pure Appl. 177 (2023), 265-298 and the ArXiv version

5. K-theory of right-angled Hecke C*-algebras
   with Adam Skalski
   Adv. Math. 407 (2022) Article No. 108559 and the ArXiv version

6. Amenability, proximality and higher order syndeticity
   with Matthew Kennedy and Guy Salomon
   Forum of Mathematics, Sigma 10 (2022) e22, 1-28 and the ArXiv version

7. An algebraic characterization of ample type I groupoids
   with Gabriel Favre
   Semigroup Forum 104 (2022), 58-71 and the ArXiv version

8. Measure equivalence for non-unimodular groups
   with Juhani Koivisto and David Kyed
   Transform. Groups 26 (2021), 327-346 and the ArXiv version

9. Cartan subalgebras in dimension drop algebras
   with Selçuk Barlak
   J. Inst. Math. Jussieu 20 (2021) No. 3, 725-755. and the ArXiv version

10. Measure equivalence and coarse equivalence for locally compact amenable groups
    with Juhani Koivisto and David Kyed
    Group, Geom. and Dyn. 15 (2021) No. 1, 223-267 and the ArXiv version

11. C*-simplicity (after Breuillard, Haagerup, Kalantar, Kennedy and Ozawa)
    Sven Raum
    Séminaire Bourbaki, exposé 1158, Astérisque 422 (2020) and the Preprint version

12. Locally compact groups acting on trees, the type I conjecture and non-amenable von Neumann algebras
    with Cyril Houdayer
    Comm. Math. Helv. 76 (2019) No. 1, 185-219 and the ArXiv version

13. C*-simplicity of locally compact Powers groups
    J. Reine Angew. Math. 748 (2019) 173-205 and the ArXiv version
    Erratum to this article

14. C*-superrigidity of 2-step nilpotent groups
    with Caleb Eckhardt
    Adv. Math. 338 (2018), 175-195 and the ArXiv version

15. Higher l²-Betti numbers of universal quantum groups
    Julien Bichon and David Kyed
    Can. Math. Bull. 61 (2018), No. 2, 225-235 and the ArXiv version

16. Traces on reduced group C*-algebras
    with Matthew Kennedy
    Bull. Lond. Math. Soc. 49 (2017) No. 6, 988-990 and the ArXiv version

17. L²-Betti numbers of rigid C*-tensor categories and discrete quantum groups
    with David Kyed, Stefaan Vaes and Matthias Valvekens
    Analysis & PDE 10 (2017), No. 7, 1757-1791 and the ArXiv version

18. On the l²-Betti numbers of universal quantum groups
    with David Kyed
    Math. Ann. 369 (2017), No. 3-4, 957–975 and the ArXiv version

19. Cocompact amenable closed subgroups: weakly inequivalent representations in the left-regular representation
    Int. Math. Res. Not., (2016), No. 24, 7671-7685 and the ArXiv version

20. The full classification of orthogonal easy quantum groups
    with Moritz Weber
    Commun. Math. Phy. 341 (2016) No. 3, 751-779 and the ArXiv

21. Easy quantum groups and quantum subgroups of a semi-direct product quantum group
    with Moritz Weber
    J. Noncommu. Geo. 9 (2015) No. 4, 1261-1293 and the ArXiv version

22. Asymptotic structure of free Araki-Woods factors
    with Cyril Houdayer
    Math. Ann. 363 (2015) No. 1-2, 237-267 and the ArXiv version

23. Baumslag-Solitar groups, relative profinite completions and measure equivalence rigidity
    with Cyril Houdayer
    J. Topol. 8 (2015), 295-313 and the ArXiv

24. The combinatorics of an algebraic class of easy quantum groups
    with Moritz Weber
    Infin. Dimens. Anal. Quantum Probab. Relat. Top. 17, No. 3 (2014) and the ArXiv version

25. Amalgamated free product type III factors with at most one Cartan subalgebra
    with Rémi Boutonnet and Cyril Houdayer
    Compositio Math. 150 (2014), 143-174 and the ArXiv version

26. On the classification of free Bogoljubov crossed product von Neumann algebras by the integers
    Groups, Geom. and Dyn. 8 (2014) No. 4, 1207-1245 and the ArXiv version

27. Tensor C*-categories arising as bimodule categories of II₁ factors
    with Sébastien Falguières
    Adv. Math. 237 (2013), 331-359 and the ArXiv version

28. Stable orbit equivalence of Bernoulli actions of free groups and isomorphism of some of their factor actions
    with Niels Meesschaert and Stefaan Vaes
    Expo. Math. 31 (2013), 274-294 and the ArXiv version

29. Isomorphisms and fusion rules of orthogonal free quantum groups and their complexifications
    Proc. Amer. Math. Soc. 140 (2012), No. 9, 3207-3218 and the ArXiv version

Other work

• Lecture notes about Creutz-Peterson's "Character rigidity for lattices and commensureators"
  Written for the Arbeitsgemeinschaft "Superrigidity" at MFO, 2014
  Lecture C3 and Lecture C4

• A connection between easy quantum groups, varieties of groups and reflection groups
  with Moritz Weber
  This is an arXiv preprint from 2012 which is not intended for publication. Please cite instead the appropriate article among my remaining work with Moritz.

• Categories of representations and classification of von Neumann algebras and quantum groups
  My PhD thesis under the supervision of Stefaan Vaes submitted in 2013 at KU Leuven.

Invited talks

Conference talks and lecture series

2024

1. November 2024
   "Cartan subalgebras from the von Neumann algebra point-of-view"
   at BIRS, Canada, during the workshop "Cartan Subalgebras in Operator Algebras, and Topological Full Groups".
2. August 2024
   "Hecke operator algebras" (4 lectures)
   at the University of Glasgow during the conference "YMC*A".
3. August 2024
   "Nuclear dimension of crossed products by free actions of connected, simply connected, nilpotent Lie groups"
   at the East China Normal Univesity during the "19th Special Week on Operator Algebras".

2023

4. Oktober 2023
   "On the unitary representation theory of groups acting on buildings of indefinite type"
   at the University of Münster, Germany, during the workshop "Totally disconnected locally compact groups: from local to global".

2022

5. November 2022
   "Detecting ideals in groups C*-algebras of lattice in Lie groups"
   at the University of Gothenburg, Sweden, during the "Swedish Operator Algebra and Noncommutative Geometry Workshop".
6. October 2022
   "Simplicity of essential groupoid C*-algebras"
   at Kiel University, Germany, during the 10th Workshop on "Operator Theoretic Aspects of Ergodic Theory".
7. September 2022
   "Simplicity of essential groupoid C*-algebras"
   at IWOATA, Kraków, Poland in the special session "Operator Spaces Techniques in Operator Algebras".
8. July 2022
   "Simplicity and the ideal intersection property for essential groupoid C*-algebras"
   at the University of Copenhagen, Denmark during the an ICM satellite conference "Operator algebras, dynamics and groups".
9. May 2022
   "Simplicity and the ideal intersection property for essential groupoid C*-algebras"
   at CIRM, Luminy, France during the workshop "Operator Algebras and Group Dynamics".

2021

10. November 2021
    "Simplicity and the ideal intersection property for essential groupoid C*-algebras"
    at the Danish-Norwegian Operator Algebras meeting, Trondheim, Norwary.

2019

11. October 2019
    "C*-superrridity"
    at MFO, Oberwolfach, Germany during the mini-workshop "Operator algebraic quantum groups".
12. September 2019
    "C*-superrridity"
    at BIRS, Banff, Canada during the workshop "Classification problems in von Neumann algebras".
13. July 2019
    "Group C*-algebras: classical and modern" (5 lectures)
    at the Sophus Lie Center, Nordfjordeid, Norway during the summer school "Analysis, Geometry and PDE".
14. June 2019
    "Cartan subalgebras in dimension drop algebras"
    at ICMAT, Madrid, Spain during the International Conference "Operator Algebras, Groups and Applications to Quantum Information".
15. February 2019
    "C*-superrigidity" (2 lectures)
    at the Fields Insitute, Toronto, Canada during the Southern Ontario Operator Algebras Seminar 2019.
16. January 2019
    "C*-superrigidity" (4 lectures)
    at IPM, Tehran, Iran during the workshop "Quantum groups".

2018

17. May 2018
    "C*-superrigidity of 2-step nilpotent groups"
    at the University of Münster, Germany, at the occasion of the conference NCGOA 2018.
18. March 2018
    "L²-Betti numbers of universal quantum groups"
    at the Université de Caen, France, during the Journées de catégories tensorielles et analyse.
19. February 2018
    "C*-superrigidity"
    at the American Institute of Mathematics, San José, CA, USA, during the Workshop "Classification of group von Neumann algebras".

2017

20. October 2017
    "Groups acting on trees: representation theory and operator algebras"
    in Sendai, Japan, during the Workshop "Ergodic and Geometric Group theory in Sendai".
21. October 2017
    "C*-superrigidity of virtually Abelian groups"
    at IMPAN, Poland, during the Workshop "Operator Algebras, Geometry, and Actions".
22. July 2017
    "C*-superrigidity of virtually Abelian groups"
    at Institut Henri Poincaré, France, during the Workshop "Von Neumann algebras and measured group theory".

2016

23. October 2016
    "Operator algebras of locally compact groups acting on trees"
    at Université de Bordeaux, France, during the Workshop "Groupes et algèbres de von Neumann".
24. August 2016
    "Non-amenable von Neumann algebras of groups acting on trees"
    in MFO, Germany, during the Workshop "C*-algebras".
25. July 2016
    "Operator algebras of locally compact groups acting on trees"
    at HIM, Bonn, Germany, during the workshop "Von Neumann algebras".
26. June 2016
    "Operator algebras of locally compact groups acting on trees"
    at Université de Paris 6, France, during the conference "Polish groups and geometry".
27. April 2016
    "Operator algebras of locally compact groups acting on trees"
    at the Mittag-Leffler Institute, Sweden, during the workshop "Classification and dynamical systems II: Von Neumann Algebras".
28. January 2016
    "Locally compact C*-simple groups"
    lecture series at IPM, Tehran, Iran at the occasion of the workshop "C*-dynamics".

2015

29. July 2015
    "The classification of orthogonal easy quantum groups"
    in Herstmonceux, UK at the occasion of the Fields institute conference on quantum groups and quantum information theory.
30. June 2015
    "Locally compact C*-simple groups"
    in MFO, Germany, during the Workshop "Noncommutative geometry".
31. June 2015
    "Powers group methods for locally compact groups acting on trees"
    in Copenhagen, Denmark at the occasion of the workshop "Representation theory of groups, quantum groups, and operator algebras".
32. May 2015
    "Powers group methods for locally compact groups acting on trees"
    in Neuchâtel, Switzerland at the Group Theory Day.
33. May 2015
    "Powers group methods for locally compact groups acting on trees"
    in Nashville, USA, at the occasion of the conference NCGOA 2015.
34. April 2015
    "Powers group methods for locally compact groups acting on trees"
    in Münster, Germany, at the occasion of the workshop "C*-algebras: Structure and Classification".

2014

35. September 2014
    "Baumslag-Solitar groups, relative profinite completions and measure equivalence rigidity"
    in Kyoto, Japan, at the occasion of the workshop on recent developments in operator algebras.
36. July 2014
    "The classification of easy quantum groups"
    in Amsterdam, the Netherlands, at the occasion of the international workshop on operator theory and its applications.
37. May 2014
    "Structure theory for von Neumann algebras: solidity"
    at the University of Franche-Comté in Besançon, France, during the journées d'analyse fonctionelle Besonçon-Neuchâtel.
38. March 2014
    "Character rigidity for lattices and commensurators (after Creutz-Peterson)"
    in MFO, Germany, during the Arbeitsgemeinschaft "Superrigidity".

2013 and before

39. December 2013
    "Baumslag-Solitar groups, relative profinite completions, and measure equivalence rigidity"
    in Caen, France, at the occasion of the Arbre de Noël.
40. January 2013
    "A duality between easy quantum groups and reflection groups"
    in Tokyo, Japan, at the occasion of a workshop on operator algebras.
41. September 2012
    "Sur la classification des produits croisés de Bogoliubov libre"
    in Lyon, France, at the occasion of the meeting of the ANR project NEUMANN.
42. May 2011
    "All finite C*-tensor categories are bimodule categories of a II₁ factor"
    in Paris, France, at the occasion of the Franco-Italien meeting of GDRE GREFI-GENCO.
43. September 2010
    "Is every finite C*-tensor category the bimodule category of a II₁ factor?"
    in Caen, France, at the occasion of the focused semester on quantum groups of the EU Noncommutative Geometry Network.
44. September 2010
    "Every finite C*-tensor category is the bimodule category of a II₁ factor"
    in Brussels, Belgium, at the occasion of the PhD day of the Belgium Mathematical Society.
45. February 2010
    "Fusion rules of free orthogonal quantum groups"
    in Cardiff, UK, at the occasion of the period on planar algebras and physics.
46. January 2010
    "Fusion rules of free orthogonal quantum groups"
    in Copenhagen, Denmark, at the occasion of the masterclass on von Neumann algebras and group actions.

Colloquium and seminar talks

2025

1. March 2025
   "Stable rank one for group C*-algebras"
   in the Operator Algebra seminar at Chalmers/University of Gothenburg.
2. March 2025
   "Stable rank one for group C*-algebras"
   in the Noncommutative Geometry and Topology seminar at the Czech Academy of Sciences, Prague.

2024

3. December 2024
   "On the structure of group C*-algebras"
   in the Oberseminar "Analysis und Theoretische Physik" at Leibniz University Hannover.

2023

4. June 2023
   "Operator algebraic group theory"
   in the MATH+ Friday Colloquium of the Berlin Mathematics Research Center.
5. March 2023
   "Right-angled Hecke algebras"
   in the joint monthly online seminar of Saarbrücken and Warsaw.
6. February 2023
   "Detecting ideals in crossed product C*-algebras of topological dynamical systems"
   in the group theory seminar the Université Catholique de Louvain-la-Neuve.
7. February 2023
   "Detecting ideals in crossed product C*-algebras of topological dynamical systems"
   in the online seminar "Functional analysis and operator algebra in Athens".
8. January 2023
   "Detecting ideals in crossed product C*-algebras of topological dynamical systems"
   in the analysis and probability seminar at the University of Gothenburg/Chalmers.

2022

9. November 2022
   "On the structure of Iwahori-Hecke (operator) algebras"
   in the Groups and Operator Algebras Seminar at the University of Copenhagen.
10. October 2022
    "On the centre of Iwahori-Hecke algebras"
    in the algebra seminar at the University of Lund/LTH.
11. May 2022
    "Simplicity and the ideal intersection property for essential groupoid C*-algebras"
    in the Operator Algebra Seminar at Seoul National University (online).
12. May 2022
    "Simplicity of essential groupoid C*-algebras"
    in the Pure Math Colloquium of the University of Sheffield (online).

2021

13. November 2021
    "Simplicity of essential groupoid C*-algebras"
    in the group theory seminar at UCLouvain.
14. October 2021
    "Simplicity of essential groupoid C*-algebras"
    in the analysis seminar at the Washington University in St. Louis (online).
15. April 2021
    "Right-angled Hecke operator algebras"
    in the seminar on ergodic and geometric group theory at EPF Lausanne (online).
16. April 2021
    "Right-angled Hecke operator algebras"
    in the operator algebra seminar at Purdue University (online).
17. March 2021
    "Right-angled Hecke operator algebras"
    in the seminar Géométrie, Groupes et Dynamiques at ENS Lyon (online).
18. March 2021
    "Superrigidity for group operator algebras"
    in the IM PAN Young Researchers Colloquium (online).
19. March 2021
    "Right-angled Hecke operator algebras and representation theory"
    in the UCSD Functional Analysis Seminar (online).
20. February 2021
    "Why group theorists could care about operator algebras"
    in the Online Seminar on Probabilistic and Geometric Group Theory (online).

2020

21. October 2020
    "Structure of Hecke von Neumann algebra and appications to representation theory"
    in the Tokyo-Kyoto online operator algebra seminar (online).
22. July 2020
    "C*-superrigidity"
    in the UK Virtual Operator Algebras Seminar (online).
23. February 2020
    "From Poisson boundaries to proximal boundaries"
    at the University of Copenhagen, Denmark, in the operator algebra seminar.

2019

24. December 2019
    "C*-superrigidity of 2-step nilpotent groups"
    at University Paris-Sud, France, in the research seminar GAN.
25. April 2019
    "C*-superrigidity of 2-step nilpotent groups"
    at the University of Glasgow, UK, in the analysis seminar.
26. March 2019
    "C*-superrigidity of 2-step nilpotent groups"
    at the University of Oslo, Norway, in the operator algebra seminar.
27. January 2019
    "C*-simpllicity"
    at IHP, Paris, France, in the Séminaire Bourbaki.

2018

28. December 2018
    "Superrigidity for group operator algebras"
    at the University of Waterloo, Canada, in the Pure Math Colloquium.
29. August 2018
    "C*-superrigidity of 2-step nilpotent groups"
    at Chalmers, Gothenburg, Sweden, in the Analysis and Probability seminar.
30. May 2018
    "C*-superrigidity of nilpotent groups"
    at EPFL, Switzerland, in the topology seminar.
31. February 2018
    "C*-superrigidity"
    at RIMS, Kyoto University, Japan.
32. February 2018
    "Cartan subalgebras in dimension drop algebras"
    at Nagoya University, Japan, in the research seminar of the analysis group.

2017

33. November 2017
    "Cartan subalgebras in dimension drop algebras"
    at Copenhagen University, Denmark, in the research seminar of the operator algebra work group.
34. November 2017
    "Groups acting on trees: representation theory and operator algebras"
    at the University of Southern Denmark, Odense, Denmark, in the research seminar of the operator algebra work group.
35. August 2017
    "C*-superrigidity of virtually abelian groups"
    at Chiba University, Japan, in the analysis seminar.
36. June 2017
    "Groups acting on trees: representation theory and operator algebras"
    at the Isaac Newton Institute, Cambridge, UK, in the operator algebras seminar.
37. May 2017
    "C*-superridigity of virtually abelian groups"
    at Université de Neuchâel, Switzerland, in the groups and analysis seminar.

2016

38. December 2016
    "On the type I conjecture for groups acting on trees"
    at EPFL, Switzerland, in the EGG seminar.
39. November 2016
    "On the type I conjecture for groups acting on trees"
    at ETH Zürich, Switzerland, in the geometry seminar.
40. April 2016
    "Algèbres d'opérateurs de groupes agissants sur les arbres"
    at Université Catholique de Louvain, Belgium, in the group theory seminar.
41. April 2016
    "C*-simplicity: from discrete to locally compact groups"
    at Hokkaido University, Japan, in the analysis research seminar.
42. March 2016
    "C*-simple and non-C*-simple locally compact groups"
    at University Paris-Sud, France, in the research seminar GAN.
43. March 2016
    "C*-simple and non-C*-simple locally compact groups"
    at Copenhagen University, Denmark, in the research seminar of the operator algebra work group.
44. March 2016
    "C*-simple and non-C*-simple locally compact groups"
    at EPFL, Switzerland, in the research seminar for ergodic and geometric group theory.

2015

45. November 2015
    "Locally compact C*-simple groups"
    at the University of Münster, Germany, in the research seminar of the noncommutative geometry workgroup.
46. October 2015
    "Locally compact C*-simple groups"
    at the University of Glasgow, Scotland, in the analysis seminar.
47. July 2015
    "Generalised symmetries of quantum spaces"
    at Keio University in Yokohama, Japan, in the monthly colloquium of the math department.
48. July 2015
    "C*-simplicity of locally compact Powers groups"
    at Ochanomizu University in Tokyo, Japan, in the operator algebras seminar.
49. January 2015
    "Free probability aspects of easy quantum groups"
    at Kyushu University in Fukuoka, Japan, in the operator algebras seminar.
50. January 2015
    "Character rigidity for lattices in higher rank Lie groups (after Creutz-Peterson and Peterson)"
    at RIMS in Kyoto, Japan, in the Kansai operator algebras seminar.

2014

51. October 2014
    "The classification of easy quantum groups"
    at Tokyo University, Japan, in the operator algebras seminar.

2013 and before

52. November 2013
    "The classification of orthogonal partition quantum groups (easy quantum groups)"
    at the University of Franche-Comté in Besançon, France, in the functional analysis seminar.
53. May 2013
    "Group von Neumann algebras of locally compact HNN-extensions"
    at the University of Oxford, UK, in the junior geometric group theory seminar.
54. December 2012
    "What is ... superrigidity?"
    at KU Leuven, Belgium, in the PhD-Colloquium.
55. November 2012
    "On the classification of free Bogoliubov crossed products of the integers"
    at Université catolique de Louvain, Belgium, in the group theory seminar.
56. October 2012
    "Tensor C*-categories arising as bimodule categories of a II₁ factor"
    at the University of Münster, Germany, in the research seminar of the noncommutative geometry workgroup.
57. June 2012
    "Von Neumann algebras and their bimodule categories"
    at Saarland University, Germany, in the functional analysis seminar.
58. May 2012
    "Les C*-catégories tensorielles, qui sont les catégories de bimodules d'un facteur II₁"
    at Institut de Mathématiques de Jussieu, Paris, France, in the operator algebras seminar.
59. April 2012
    "Tensor C*-categories arising as bimodule categories of II₁ factors"
    at KU Leuven, Belgium, in the operator algebras seminar.
60. June 2009
    "On the corepresentation theory of complexified quantum groups"
    at KU Leuven, Belgium, in the operator algebras seminar.

Conference Organisation

May 2024	Workshop "Point sets: Dynamics, sampling, and operator algebras" Organised at the University of Oslo
May 2023	School and workshop on Noncommutative Geometry and Operator algebras Organised at the Hausdorff Centre for Mathematics in Bonn
March 2023	Mini-workshop on operator algebras and noncommutative geometry Meeting of Swedish operator algebraists and noncommutative geometers at Stockholm University
November 2022	Mini-workshop on operator algebras and noncommutative geometry Meeting of Swedish operator algebraists and noncommutative geometers at Chalmers/University of Gothenburg
August 2022	Operator algebras and noncommutative geometry Parallel session at the Nordic Congress of Mathematics
May 2022	C*-algebras and geometry of groups and semigroups Workshop at the University of Oslo
March 2022	Noncommutativity in the north Workshop at Chalmers/University of Gothenburg
January 2022	Mini-workshop on operator algebras and noncommutative geometry Meeting of Swedish operator algebraists and noncommutative geometers at Chalmers/University of Gothenburg
March 2021	C*-algebras and geometry of groups and semigroups Online workshop
May 2017	Approximate lattices Two-day reading group joint between EPFL and the University of Neuchâtel
July 2016	Young Mathematicians in C*-Algebras Co-organiser responsible for funding, scientific organisation and social events

Teaching and supervision

Taught courses

2024/2025 Winter	Algebra Reflection groups
2024 Summer	Algebra und Zahlentheorie Lineare Algebra und analytische Geometrie II
2023/2024 Winter	Algebra Lineare Algebra und analytische Geometrie
2023 Summer	Algebra and number theory Geometric group theory Lie algebras (seminar)
2022 Autumn	Expander graphs
2022 Spring	Linear algebra
2021 Autumn	Linear algebra
2021 Spring	Geometric group theory Complex analysis
2020 Spring	Introduction to operator algebras Foundations of analysis
2019 Autumn	Combinatorics
2019 Spring	Foundations of analysis Ordinary differential equations
2018 Spring	Lie groups Homology and cohomology
2017 Autumn	Linear algebra for engineers
2017 Spring	Abstract harmonic analysis
2016 Autumn	Linear algebra for engineers
2016 Summer	Abstract harmonic analysis
2015 Winter	Von Neumann algebras and measured group theory

Supervision of PhD students

2019 - 2023

Gabriel Favre

Supervision of Master theses

2022	C*-simplicity of discrete groups and étale groupoids
2022	Group C*-algebras of Heisenberg groups and C*-rigidity
2017/18	On groups of type I
2016/17	C*-simplicity and factorial group von Neumann algebras
2011/12	Equivalence relations with prescribed fundamental group (co-supervision)
2010/11	Orbit equivalence of Bernoulli actions over free groups (co-supervision)
2009/10	There is no universal II1 factor (co-supervision)

Supersion of Bachelor theses

2021/22	Number systems beyond the reals (teacher student) The search for orthogonal Latin squares (teacher student) Measure-theoretic Probability
2020/21	Decomposition theory for zero-sum games (math-economy student) Mathematical billards (teacher student) The logic behind Kőnig's lemma Quivers, path algebras and Gabriel's theorem Which schools would take me? Truth-telling in school choice with admission probability uncertainty
2019/20	Quantum computing: From Shor’s algorithm to the hidden subgroup problem The travelling salesman in Sweden (teacher student) Classical finite simple groups The spectral theorem for normal operators
2018/19	Wallpaper groups (teacher student)
2017/18	K-theory and Bott periodicity
2016/17	Classification of closed surfaces

Teaching material

Lie groups. Spring term 2018

• Exercise sheet 1
• Exercise sheet 2
• Exercise sheet 3
• Exercise sheet 4
• Exercise sheet 5
• Exercise sheet 6
• Exercise sheet 7
• Exercise sheet 8
• Exercise sheet 9
• Exercise sheet 10
• Exercise sheet 11
• Exercise sheet 12
• Exercise sheet 13

Homology and Cohomology. Spring term 2018

• Exercise sheet 1
• Exercise sheet 2
• Exercise sheet 3
• Exercise sheet 4
• The first assignment and the LaTeX code
• Exercise sheet 5
• Exercise sheet 6
• Exercise sheet 7
• Exercise sheet 8
• Handwritten notes on the local degree
• Exercise sheet 9 and a link related to Exercises 1 and 2
• Exercise sheet 10
• Exercise sheet 11
• The second assignment
• An excellent solution to the first assignment
• An excellent LaTeX code for the first assignment
• Exercise sheet 12
• Trial exam

Abstract harmonic analysis. Spring term 2017

• Lecture notes (version from 18th May 2017)

Abstrakte harmonische Analysis. Sommersemester 2016

• Übungsblatt 1
• Übungsblatt 2
• Übungsblatt 3
• Übungsblatt 4
• Übungsblatt 5
• Übungsblatt 6
• Übungsblatt 7
• Übungsblatt 8
• Übungsblatt 9
• Übungsblatt 10
• Übungsblatt 11
• Übungsblatt 12
• Übungsblatt 13

Von Neumann Algebren und messbare Gruppentheorie. Wintersemester 2015/16

• Announcement (in German)
• Lecture notes (version from 4th February 2016)

Vita

Born on 9th April 1985 in Kassel, Germany.

Current Employment

Since Apr 2023

W2-Professor at the University of Potsdam, Germany

Previous Employment

Sep 2018 - Mar 2023	Associate Professor at Stockholm University, Sweden
Jun - Jul 2021	Visiting Professor at IM PAN, Poland
Sep - Dec 2020	Visiting Professor at IM PAN, Poland
2016 - 2018	Lecturer at EPFL, Switzerland
2015 - 2016	Marie Curie International Outgoing Fellow at the University of Münster, Germany
2014 - 2015	Marie Curie International Outgoing Fellow at RIMS, Kyoto, Japan
2013 - 2014	Post doctoral scholar at ENS Lyon, France
2009 - 2013	PhD scholar at KU Leuven, Belgium
2007 - 2009	Student teaching assistant at the University of Münster

Education

Oct 2019	Docent in Mathematics at Stockholm University, Sweden
Sep 2009 - Jun 2013	PhD in Mathematics at KU Leuven, Belgium
Oct 2005 - May 2009	Diplom Mathematik at the University of Münster, Germany

Languages

German	Mother tongue
English	Fluent
French	Fluent (B2)
Dutch	Fluent (C1)
Swedish	Fluent
Persian	Basic knowledge
Japanese	Baisc knowledge (JLPT N5)

Links

Places

• ENS Lyon, UMPA
• EPFL, Section of mathematics
• KU Leuven, Department of mathematics
• Polish Academy of Sciences, Institute of Mathematics
• Stockholm University, Department of Mathematics
• University of Kyoto, Research Institute for Mathematical Sciences
• University of Münster, Department of Mathematics
• University of Potsdam, Institute of Mathematics

Family

• My brother, who is a mathematician too
• My wife, who is also a mathematician