Martijn Caspers

Research interests

• Quantum groups
• Operator algebras
• Operator spaces and their approximation properties
• Non-commutative Lp-spaces
• Harmonic analysis on non-commutative spaces

Papers and preprints

Any comment, suggestion or question is more than welcome. "Final version" indicates that the ArXiv-version agrees with the version that was sent for the publication process.

Preprints

• "On the best constants of Schur multipliers of second order divided difference functions".
  With Jesse Reimann.
  preprint.
  
  
• "Classification of right-angled Coxeter groups with a strongly solid von Neumann algebra".
  With Matthijs Borst.
  preprint.
  
  

Papers (in press)

• "Local and multilinear noncommutative de Leeuw theorems".
  with Bas Janssens, Amudhan Krishnaswamy-Usha and Lukas Miaskiwskyi.
  Math. Ann. 388 (2024), no. 4, 4251-4305..
  preprint (final version).
  
  
• "Bimodule coefficients, Riesz transforms on Coxeter groups and strong solidity".
  with Matthijs Borst and Mateusz Wasilewski.
  Accepted for Groups, Geometry and Dynamics.
  preprint (final version).
  
  
• "A Sobolev estimate for radial Lp-multipliers on a class of semi-simple Lie groups".
  Trans. Amer. Math. Soc. 376 (2023), no. 12, 8919–8938.
  preprint (final version).
  
  
• "On the isomorphism class of q-Gaussian W*-algebras for infinite variables".
  preprint (final version).
  C. R. Math. Acad. Sci. Paris 361 (2023), 1711–1716.
  
  
• "Multilinear transference of Fourier and Schur multipliers acting on non-commutative Lp-spaces".
  with Amudhan Krishnaswamy-Usha and Gerrit Vos.
  Canad. J. Math. 75 (2023), no. 6, 1986–2006.
  preprint.
  
  
• "Overcompleteness of coherent frames for unimodular amenable groups".
  with Jordy Timo van Velthoven.
  Ark. Mat. 61 (2023), no. 2, 277-299.
  preprint.
  
  
• "Relative Haagerup property for arbitrary von Neumann algebras".
  with Mario Klisse, Adam Skalski, Gerrit Vos and Mateusz Wasilewski.
  Adv. Math. 421 (2023), Paper No. 109017.
  preprint.
  
  
• "On the isomorphism class of q-Gaussian C*-algebras for infinite variables".
  with Matthijs Borst, Mario Klisse and Mateusz Wasilewski.
  Proc. Amer. Math. Soc. 151 (2023), no. 2, 737–744.
  preprint (final version).
  
  
• "Riesz transforms on compact quantum groups and strong solidity".
  J. Inst. Math. Jussieu 21 (2022), no. 6, 2135–2171
  preprint (final version).
  
  
• "Density conditions with stabilizers for lattice orbits of Bergman kernels on bounded symmetric domains".
  with Jordy Timo van Velthoven.
  Math. Z. 302, 609–628 (2022).
  preprint (final version).
  
  
• "BMO spaces of sigma-finite von Neumann algebras and Fourier-Schur multipliers on quantum SU(2)".
  with Gerrit Vos.
  Studia Math. 262 (2022), no. 1, 45–91.
  preprint (final version).
  
  
• "Weak (1,1) estimates for multiple operator integrals and generalized absolute value functions".
  with Fedor Sukochev and Dmitriy Zanin.
  Israel J. Math. 244 (2021), no. 1, 245–271.
  preprint (final version).
  
  
• "L2-cohomology, derivations and quantum Markov semi-groups on q-Gaussian algebras".
  with Yusuke Isono and Mateusz Wasilewski.
  Int. Math. Res. Not. IMRN 2021, no. 9, 6405–6441.
  preprint (final version).
  
  
• "Gradient forms and strong solidity of free quantum groups".
  Math. Ann. 379 (2021), no. 1-2, 271–324.
  preprint (final version).
  
  
• "Graph product Khintchine inequalities and Hecke C*-algebras: Haagerup inequalities, (non)simplicity, nuclearity and exactness".
  with Mario Klisse and Nadia Larsen.
  J. Funct. Anal. 280 (2021), no. 1, 108795.
  preprint (final version).
  
  
• "Absence of Cartan subalgebras for right-angled Hecke von Neumann algebras".
  Anal. PDE 13 (2020), no. 1, 1--28.
  preprint (final version), erratum.
  
  
• "BMO-estimates for non-commtutative vector valued Lipschitz functions".
  with Marius Junge, Fedor Sukochev, Dima Zanin.
  J. Funct. Anal. 278 (2020), no. 3, 108317.
  preprint (final version).
  
  
• "On MASAs in q-deformed von Neumann algebras".
  with Adam Skalski and Mateusz Wasilewski.
  Pacific J. Math. 302 (2019), no. 1, 1--21.
  preprint (final version).
  
  
• "Weak type commutator and Lipschitz estimates: resolution of the Nazarov-Peller conjecture".
  with Denis Potapov, Fedor Sukochev and Dmitriy Zanin.
  Amer. J. Math. 141 (2019), no. 3, 593–610.
  preprint (final version).
  
  
• "On the complete bounds of Lp-Schur multipliers".
  with Guillermo Wildschut.
  Arch. Math. (Basel) 113 (2019), no. 2, 189–200.
  preprint (final version).
  
  
• "On C*-completions of discrete quantum group rings".
  with Adam Skalski.
  Bull. London Math. Soc. 51 (2019), no. 4, 691-704.
  preprint (final version).
  
  
• "Harmonic analysis and BMO-spaces of free Araki-Woods factors".
  Studia Math. 246 (2019), no. 1, 71–107.
  preprint (final version).
  
  
• "Weak type operator Lipschitz and commutator estimates for commuting tuples".
  with Fedor Sukochev and Dmitriy Zanin.
  Ann. Inst. Fourier (Grenoble) 68 (2018), no. 4, 1643–1669.
  preprint (final version).
  
  
• "Graph products of operator algebras".
  with Pierre Fima.
  J. Noncommut. Geom. 11 (2017), no. 1, 367-411.
  preprint (final version).
  
  
• "Connes embeddability of graph products".
  Infin. Dimens. Anal. Quantum Probab. Relat. Top. 19 (2016), no. 1, 1650004, 13 pp.
  preprint (final version).
  
  
• "Operator biflatness of the L1-algebras of compact quantum groups".
  with Hun Hee Lee and Eric Ricard.
  J. Reine Angew. Math. 700 (2015), 235-244.
  preprint (final version).
  
  
• "Schur and Fourier multipliers of an amenable group acting on non-commutative Lp-spaces".
  with Mikael de la Salle.
  Trans. Amer. Math. Soc. 367 (2015), no. 10, 6997-7013.
  preprint (final version).
  
  
• "The Haagerup approximation property for von Neumann algebras via quantum Markov semigroups and Dirichlet forms".
  with Adam Skalski.
  Comm. Math. Phys. 336 (2015), no. 3, 1637-1664.
  preprint (final version).
  
  
• "Noncommutative de Leeuw theorems".
  with Javier Parcet, Mathilde Perrin, Eric Ricard.
  Forum of Mathematics - Sigma 3 (2015), e21.
  preprint (not final but journal is open access).
  
  
• "The Haagerup property for arbitrary von Neumann algebras".
  with Adam Skalski.
  Int. Math. Res. Not. IMRN 2015, no. 19, 9857-9887.
  preprint (final version).
  
  
• "Weak type estimates for the absolute value mapping".
  with Denis Potapov, Fedor Sukochev and Dima Zanin.
  J. Operator Theory 73 (2015), no. 2, 361-384.
  preprint (final version).
  
  
• "The best constants for operator Lipschitz functions on Schatten classes".
  with Stephen Montgomery-Smith, Denis Potapov and Fedor Sukochev.
  J. Funct. Anal. 267 (2014), no. 10, 3557-3579.
  preprint (final version).
  
  
• "Weak amenability of locally compact quantum groups and approximation properties of extended quantum SU(1,1)".
  Comm. Math. Phys. 331 (2014), no. 3, 1041-1069.
  preprint (final version).
  
  
• "Generalisations of the Haagerup approximation property to arbitrary von Neumann algebras".
  with Rui Okayasu, Adam Skalski, Reiji Tomatsu.
  C. R. Acad. Sci. Paris, Ser. I 352 (2014) 507-510
  preprint (final version).
  
  
• "The Walsh basis in the Lp-spaces of hyperfinite III_\lambda factors, 0 < \lambda <=1".
  with Denis Potapov and Fedor Sukochev.
  J. Math. Anal. Appl. 408 (2013), 154-164
  preprint (final version), journal.
  
  
• "The L^p-Fourier transform on locally compact quantum groups".
  J. Operator Theory 69 (2013), 161-193
  preprint (final version), journal
  
  
• "Spherical Fourier transforms on locally compact quantum Gelfand pairs".
  SIGMA 7 (2011), 087, 39 pages.
  paper (final version), journal.
  
  
• "Modular properties of matrix coefficients of corepresentations of a locally compact quantum group".
  Together with Erik Koelink.
  J. Lie Theory 21 (2011), no. 4, 905-928.
  preprint (final version), journal.
  
  
• "Intuitionistic quantum logic of an n-level system".
  Together with Chris Heunen, Klaas Landsman and Bas Spitters.
  Foundations of Physics 39 (2009), No. 7, 731-759.
  preprint (final version), journal.
  
  

Other

• "Profcast" interview with Dave Boomkens and Marieke Kootte (in Dutch), 2021.
  See spotify or (soon) the webpage.
  My thanks to Klaas Landsman and Erik Koelink for their contributions!
  
  
• "Weight theory for ultraproducts".
  preprint.
  Preprint contains a mistake and the main result should be extended to non-semifinite weights. I am happy to discuss with anyone who has ideas.
  
  
• "Quantum Symmetry". 2021
  Oberwolfach Snapshot - popular article describing the fundamental idea of quantum groups.
  link.
  
  
• "Mini-workshop: operator algebraic quantum groups". 2020.
  with Michael Brannan, Moritz Weber, Anna Wysoczanska-Kula.
  Oberwolfach Rep. 16 (2020), no. 4, 2821–2867.
  
  
• "On the endpoints of De Leeuw restriction theorems". 2018.
  Chapter in Festschrift on the occassion of Ben de Pagter's 65th anniversary.
  link.
  
  
• "Locally compact quantum groups". Lecture notes, Bedlewo 2015.
  Banach Center Publications 111 (2017), 153-184.
  link.
  
  
• "Noncommutative De Leeuw theorems". Noncommutative geometry. Oberwolfach Reports 2 (2015), 1631-1700.
  link.
  
  
• "Hecke von Neumann algebras, operator spaces and absence of Cartan subalgebras". Noncommutative geometry and operator spaces in interaction. Oberwolfach Reports, 2016.
  link.
  
  
• "Gradient forms and strong solidity of free quantum groups". Interactions between Operator Space Theory and Quantum Probability with Applications to Quantum Information. Oberwolfach Reports, 2018.
  link.
  
  
• "Quantum groups and special functions". Winter school in Bizerte, Tunisia, 2010.
  Prepared together with Erik Koelink.
  notes.
  
  

Thesis

• "Non-commutative integration on locally compact quantum groups" (PhD Thesis 2012).
  Adviser: Erik Koelink
  Download: Thesis.
  
  
  
• "Gelfand spectra of C*-algebras in topos theory" (MSc. Thesis 2008).
  Under supervision of Klaas Landsman.
  Awarded with the GQT MSc. thesis prize.