Research

Talks can be found on my YouTube channel.

Preprints 

• The harmonic oscillator on the Moyal-Groenewold plane: an approach via Lie groups and twisted Weyl tuples (joint with Cédric Arhancet, Lukas Hagedorn, and Christoph Kriegler)

This is a link to the ArXiV version 1 (December 2023). A few more results may be added before submission to a journal.

• Stochastic and deterministic parabolic equations with bounded measurable coefficients in space and time: well-posedness and maximal regularity (joint with Pascal Auscher)

This is a link to the ArXiV version (October 2023).  The actual paper has been submitted.

• A note on Rubio de Francia's extrapolation in tent spaces and applications (joint with Jose Maria Martell)

This is a link to the ArXiV version (August 2023).  The actual paperhas been published  in Journal of Mathematical Analysis and Applications Volume 537, Issue 2, 128312 (2024).

• Thermal time as an unsharp observable (joint with Jan van Neerven).

This is a link to the ArXiV version (June 2023).  The actual paper has been published  in Journal of Mathematical Physics 65, 032105 (2024).

• Function spaces for decoupling (joint with Andrew Hassell, Jan Rozendaal, and Po Lam Yung)

This is a link to the ArXiV version 1 (February 2023). A few more results may be added before submission to a journal.

• Spectral multiplier theorems for abstract harmonic oscillators on UMD lattices (joint with Jan van Neerven and Himani Sharma).

This is a link to the ArXiV version (January 2022). The actual paper has been published in Comptes Rendus - Mathématique Volume 361 (2023), 835-846.
Here is a link to a related TALK.

• Lp estimates for wave equations with specific Lipschitz coefficients (joint with Dorothee Frey)

This is a link to the ArXiV version (October 2020, with an important upgrade in April 2021).
The actual paper has been submitted. Here is a link to a TALK on the paper.

• Off singularity bounds and Hardy spaces for Fourier integral operators (joint with Andrew Hassell and Jan Rozendaal)

This is a link to the ArXiV version (November 2018). The actual paper has been published  in Transactions of the American Mathematical Society 373 (2020), 5773-5832 .

• Stochastic maximal regularity for rough time-dependent problems (joint with Mark Veraar)

This is a link to the ArXiV version (October 2018). The actual paper has been published in Stochastics and PDE: Analysis and Computations 7 (2019) 541-597. 

• The Weyl calculus for group generators satisfying the canonical commutation relations (joint with Jan van Neerven)

This is a link to the ArXiV version (June 2018). The actual paper has been published in Journal of Operator Theory 83 (2020) 253-298.  Here is a link to a TALK on the paper. 

• Weyl calculus with respect to the Gaussian measure and restricted L^p-L^q boundedness of the Ornstein-Uhlenbeck semigroup in complex time (joint with Jan van Neerven)

This is a link to the ArXiV version (February 2017). The actual paper has been published in  Bulletin de la Société Mathématique de France 146 (2018) 691-712. 

• On existence and uniqueness for non-autonomous parabolic Cauchy problems with rough coefficients (joint with Pascal Auscher and Sylvie Monniaux)

This is a link to the ArXiV version (November 2015). The actual paper has been published in  Annali della Scuola Normale Superiore di Pisa XIX (2019) 387-471. 

• Finite speed of propagation and off-diagonal bounds for Ornstein-Uhlenbeck operators in infinite dimensions (joint with Jan van Neerven)

This is a link to the ArXiV version (July 2015). The actual paper has been published in Annali di Matematica Pura ed Applicata 195 (2016) 1889-1915. 

• Conical square function estimates and functional calculi for perturbed Hodge-Dirac operators in Lp (joint with Dorothee Frey and Alan McIntosh)

This is a link to the ArXiV version  (July 2014). The actual paper has been published in Journal d'Analyse Mathematique 134 (2018) 399-453. 

• Maximal and quadratic Gaussian Hardy spaces 

This is a link to the ArXiV version (March 2012). The actual paper has been published in Revista Matematica Iberoamericana 30 (2014) 79-108. 

• Singular integral operators on tent spaces (joint with Pascal Auscher, Christoph Kriegler, and Sylvie Monniaux) 

This is a link to  the ArXiV version (December 2011). The actual paper has been published in Journal of Evolution Equations 12 (2012) 741-765. 

• Conical maximal Lp-regularity for stochastic convolutions (joint with Pascal Auscher and Jan van Neerven) 

This is a link to  the ArXiV version (December 2011). The actual paper has been published in Mathematische Annalen 359 (2014) 863-889.

• The maximal regularity operator on tent spaces (joint with Pascal Auscher and Sylvie Monniaux) 

This is a link to the ArXiV version (November 2010). The actual paper has been published in Communication in Pure and Applied Analysis 11 (2012) 2213-2219. 

• Non-tangential maximal functions and conical square functions with respect to the Gaussian measure (joint with Jan Maas and Jan van Neerven) 

This is a link to the ArXiV version (March 2010). The actual paper has been published in Publicacions Matematiques 55 (2011) 313-341. 

• Whitney coverings and the tent spaces T^{1,q} for the Gaussian measure (joint with Jan Maas and Jan van Neerven) 

This is a link to the ArXiV version (February 2010). The actual paper has been published in Arkiv for Matematik 50 (2012) 379-395. . 

• Holomorphic functional calculus of Hodge-Dirac operators in Lp (joint with Tuomas Hytonen and Alan McIntosh) 

This is a link to the the ArXiV version (July 2009). The actual paper has been published in Journal of Evolution Equations 11 (2011) 71-105. 

• Conical square function estimates in UMD Banach spaces (joint with Tuomas Hytonen and Jan Van Neerven) 

This is a link to the ArXiV version (September 2007). The actual paper has been published in Journal d'Analyse Mathematique 106 (2008) . 

• Kato's square root problem in Banach spaces (joint with Tuomas Hytonen and Alan McIntosh) 

This is a link to the ArXiV version (February 2007). The actual paper has been published in Journal of Functional Analysis 254 (2008) . 

• Vector-valued multiparameter singular integrals and pseudodifferential operators (joint with Tuomas Hytonen) 

This is a preprint version (October 2005) in pdf. The actual paper has been published in Advances in Mathematics 217 (2008) . 

• Some remarks on l1 and l-infinity maximal regularity for power-bounded operators (joint with Nigel Kalton) 

This is a preprint version (August 2005) in pdf. The actual paper has been published in Journal of the Australian Math. Society 84 (2008) . 

• Pseudodifferential operators on Bochner spaces and an application (joint with Zeljko Strkalj) 

This is a preprint version (July 2004) in pdf. The actual paper has been published in Mathematische Zeitschrift 253 (2006) . 

• Maximal regularity of evolution equations on discrete time scales 

This is a preprint version (December 2003) in pdf. The actual paper has been published in Journal of Mathematical Analysis and Applications 304/1 (2005). 

• Discrete time analytic semi-groups and the geometry of Banach spaces

This is a preprint version (December 2001) in pdf. The actual paper has been published in Semigroup Forum 67 (2003) . 

Editorial work 

• Editor of  Bulletin of the Australian Mathematical Society (since 2019)

• Editor of  Complex Analysis and Operator Theory (since 2014)

• (with J. Ball, M. Dritschel, T. ter Elst, D. Potapov) Operator theory in harmonic and non-commutative analysis. Volume 240 of  Operator Theory: Advances and Applications Birkhauser 2014.

• (with Alan McIntosh) Proceedings of the CMA/AMSI ``Asymptotic Geometric Analysis, Harmonic Analysis and Related Topics" Research Symposium. Volume 42 of the Proceedings of the CMA .

Thesis 

• Harmonic Analysis of Banach space valued functions in the study of parabolic evolution equations 

This is my PhD thesis. The first few pages are in French but, besides that, it is written in English. My advisers were Nigel Kalton at the University of Missouri-Columbia and Gilles Lancien at the Universite de Franche-Comte in Besancon. 

• Elements de classification lipschitzienne et uniforme des espaces de Banach et application 

This is my Master thesis, written in French with Gilles Lancien as adviser.