Sven Raum

Department of Mathematics
Stockholm University
SE-106 91 Stockholm
Sweden

Email: raum@math.su.se
Public key

ORCID: 0000-0002-9188-9890
ResearcherID: K-6725-2017

I am Sven Raum, working as associate professor at Stockholm University in Sweden. My research focuses on the interaction between operator algebras, group theory and representation theory. The major link between these topics is created by group operator algebras, such as the reduced group C*-algebras and the group von Neumann algebra. Both can be associated with arbitrary locally compact groups. Other relevant topics for my work are C*-tensor categories, quantum groups, topolgical dynamics, ergodic theory and totally disconnected locally compact groups.

Besides research mathematics, I enjoy thinking about didactics of higher education. In my free time, I like learning languages, doing sports and cooking.

HAOART Seminar

Due to the Corona pandemic, our seminar on Harmonic Analysis, Operator Algebras and Representation Theory (pronounced "Howard") is currently suspended in favor of Wednesday's Zoom Seminar.

All abstracts can be found in the SMC calender: Link

Publications

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

Preprints

Research articles

  1. Measure equivalence and coarse equivalence for locally compact amenable groups
    with Juhani Koivisto and David Kyed
    To appear in Group, Geom. and Dyn.
    ArXiv (2017)

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

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

  4. Cartan subalgebras in dimension drop algebras
    with Selçuk Barlak
    J. Inst. Math. Jussieu (2019) and the ArXiv version

  5. 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

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

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

  8. 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

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

  10. 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

  11. 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

  12. 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

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

  14. 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

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

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

  17. 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

  18. 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

  19. 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

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

  21. 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

  22. 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

Talks

Conference talks and lecture series

    2019

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

    7. 2018

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

    10. 2017

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

    13. 2016

  13. 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".
  14. August 2016:
    "Non-amenable von Neumann algebras of groups acting on trees"
    in MFO, Germany, during the Workshop "C*-algebras".
  15. July 2016:
    "Operator algebras of locally compact groups acting on trees"
    at HIM, Bonn, Germany, during the workshop "Von Neumann algebras".
  16. June 2016:
    "Operator algebras of locally compact groups acting on trees"
    at Université de Paris 6, France, during the conference "Polish groups and geometry".
  17. 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".
  18. January 2016:
    "Locally compact C*-simple groups"
    lecture series at IPM, Tehran, Iran at the occasion of the workshop "C*-dynamics".

    19. 2015

  19. 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.
  20. June 2015:
    "Locally compact C*-simple groups"
    in MFO, Germany, during the Workshop "Noncommutative geometry".
  21. 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".
  22. May 2015:
    "Powers group methods for locally compact groups acting on trees"
    in Neuchâtel, Switzerland at the Group Theory Day.
  23. May 2015:
    "Powers group methods for locally compact groups acting on trees"
    in Nashville, USA, at the occasion of the conference NCGOA 2015.
  24. 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".

    25. 2014

  25. 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.
  26. 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.
  27. 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.
  28. March 2014:
    "Character rigidity for lattices and commensurators (after Creutz-Peterson)"
    in MFO, Germany, during the Arbeitsgemeinschaft "Superrigidity".

    29. 2013 and before

  29. December 2013:
    "Baumslag-Solitar groups, relative profinite completions, and measure equivalence rigidity"
    in Caen, France, at the occasion of the Arbre de Noël.
  30. January 2013:
    "A duality between easy quantum groups and reflection groups"
    in Tokyo, Japan, at the occasion of a workshop on operator algebras.
  31. 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.
  32. 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.
  33. 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.
  34. 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.
  35. February 2010:
    "Fusion rules of free orthogonal quantum groups"
    in Cardiff, UK, at the occasion of the period on planar algebras and physics.
  36. 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

    2021

  1. March 2021:
    "Right-angled Hecke operator algebras"
    in the seminar Géométrie, Groupes et Dynamiques at ENS Lyon.
  2. March 2021:
    "Superrigidity for group operator algebras"
    in the IM PAN Young Researchers Colloquium.
  3. March 2021:
    "Right-angled Hecke operator algebras and representation theory"
    in the UCSD Functional Analysis Seminar.
  4. February 2021:
    "Why group theorists could care about operator algebras"
    in the Online Seminar on Probabilistic and Geometric Group Theory.

    5. 2020

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

    8. 2019

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

    12. 2018

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

    17. 2017

  17. November 2017:
    "Cartan subalgebras in dimension drop algebras"
    at Copenhagen University, Denmark, in the research seminar of the operator algebra work group.
  18. 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.
  19. August 2017:
    "C*-superrigidity of virtually abelian groups"
    at Chiba University, Japan, in the analysis seminar.
  20. June 2017:
    "Groups acting on trees: representation theory and operator algebras"
    at the Isaac Newton Institute, Cambridge, UK, in the operator algebras seminar.
  21. May 2017:
    "C*-superridigity of virtually abelian groups"
    at Université de Neuchâel, Switzerland, in the groups and analysis seminar.

    22. 2016

  22. December 2016:
    "On the type I conjecture for groups acting on trees"
    at EPFL, Switzerland, in the EGG seminar.
  23. November 2016:
    "On the type I conjecture for groups acting on trees"
    at ETH Zürich, Switzerland, in the geometry seminar.
  24. April 2016:
    "Algèbres d'opérateurs de groupes agissants sur les arbres"
    at Université Catholique de Louvain, Belgium, in the group theory seminar.
  25. April 2016:
    "C*-simplicity: from discrete to locally compact groups"
    at Hokkaido University, Japan, in the analysis research seminar.
  26. March 2016:
    "C*-simple and non-C*-simple locally compact groups"
    at University Paris-Sud, France, in the research seminar GAN.
  27. 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.
  28. March 2016:
    "C*-simple and non-C*-simple locally compact groups"
    at EPFL, Switzerland, in the research seminar for ergodic and geometric group theory.

    29. 2015

  29. November 2015:
    "Locally compact C*-simple groups"
    at the University of Münster, Germany, in the research seminar of the noncommutative geometry workgroup.
  30. October 2015:
    "Locally compact C*-simple groups"
    at the University of Glasgow, Scotland, in the analysis seminar.
  31. July 2015:
    "Generalised symmetries of quantum spaces"
    at Keio University in Yokohama, Japan, in the monthly colloquium of the math department.
  32. July 2015:
    "C*-simplicity of locally compact Powers groups"
    at Ochanomizu University in Tokyo, Japan, in the operator algebras seminar.
  33. January 2015:
    "Free probability aspects of easy quantum groups"
    at Kyushu University in Fukuoka, Japan, in the operator algebras seminar.
  34. 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.

    35. 2014

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

    36. 2013 and before

  36. 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.
  37. May 2013:
    "Group von Neumann algebras of locally compact HNN-extensions"
    at the University of Oxford, UK, in the junior geometric group theory seminar.
  38. December 2012:
    "What is ... superrigidity?"
    at KU Leuven, Belgium, in the PhD-Colloquium.
  39. November 2012:
    "On the classification of free Bogoliubov crossed products of the integers"
    at Université catolique de Louvain, Belgium, in the group theory seminar.
  40. 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.
  41. June 2012:
    "Von Neumann algebras and their bimodule categories"
    at Saarland University, Germany, in the functional analysis seminar.
  42. 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.
  43. April 2012:
    "Tensor C*-categories arising as bimodule categories of II1 factors"
    at KU Leuven, Belgium, in the operator algebras seminar.
  44. June 2009:
    "On the corepresentation theory of complexified quantum groups"
    at KU Leuven, Belgium, in the operator algebras seminar.

Teaching and supervision

Taught courses

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

Since 2019 Gabriel Favre

Supervision of Master theses

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

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

Homology and Cohomology. Spring term 2018

Abstract harmonic analysis. Spring term 2017

Abstrakte harmonische Analysis. Sommersemester 2016

Von Neumann Algebren und messbare Gruppentheorie. Wintersemester 2015/16

Vita

Born on 9th April 1985 in Kassel, Germany.

Current Employment

Since Sep 2018 Associate Professor at Stockholm University, Sweden

Previous Employment

Sep - Dec 2020 Visiting Professor at IMPAN, 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 Good
Japanese Baisc knowledge (JLPT N5)
Persian Basic knowledge