Publications

In Preparation:

"Equidistribution of solutions of nonlinear eigenvalue problems on tori"

"Multifractal scaling and the Euler equations on 3-tori"

Mathematics

"Proving multifractality for intermediate quantum systems",  10 pp., arXiv, Proceedings of the 11th workshop on Quantum Chaos and Localisation Phenomena, 

Acta Phys. Pol. A., to appear

"Algebraic delocalization for the Schrödinger equation on large tori", 10 pp., arXiv, submitted

(with J. P.  Keating) "Multifractal eigenfunctions for quantum star graphs", 12 pp., arXiv, under review

"Quantitative equidistribution of eigenfunctions for toral Schrödinger operators", 15 pp., arXiv, Rev. Math. Phys., accepted

(with J. P. Keating) "Multifractal eigenfunctions for a singular quantum billiard, 28 pp., arXiv, Comm. Math. Phys.  Vol. 389 (2022), 543-569

(with T. Letendre) "Random moments for the new eigenfunctions of point scatterers on flat tori", 54 pp., arXiv, Ann. H. Poincaré Vol. 22 (2021), 1783-1836, https://doi.org/10.1007/s00023-021-01032-5

(with O. Friedland) "Superscarred quasimodes on flat surfaces with conical singularities", 23 pp., arXiv, Studia Math. (2022), doi: 10.4064/sm201008-23-6 

(with P. Kurlberg) "Non-Gaussian waves in Seba's billiard", 16 pp., arXiv, IMRN (2021), https://doi.org/10.1093/imrn/rnab289 

(with O. Friedland) "Scarred quasi-modes on translation surfaces", 10 pp., arXiv

(with G. Rivière) "The Quantum Loschmidt echo on flat tori", 34 pp.,  arXiv, Nonlinearity Vol. 32 (2019), No. 6, 2094-2127, doi.org/10.1088/1361-6544/ab0465

"Delocalization for random displacement models with Dirac masses", 18 pp., arXiv, under review

"Uniformly distributed eigenfunctions on flat tori with random impurities", 16 pp., arXiv

(with P. Kurlberg) "Superscars in the Seba billiard", 20 pp., arXiv, J. Eur. Math. Soc. Vol. 19 (2017), 2947-2964, doi: 10.4171/JEMS/732

"On the spectral geometry of tori with random impurities", 8 pp., arXiv, Proc. Journées É. D. P. (2015), exp. No. 11, 1-7, doi: 10.5802/jedp.640

(with P. Kurlberg) "Quantum Ergodicity for point scatterers on arithmetic tori", arXiv, GAFA 24 (2014), No. 5, 1565-90, doi: 10.1007/s00039-014-0275-6

"Quantum Chaos for point scatterers on flat tori", arXiv, 13 pp., Phil. Trans. R. Soc. A 372 (2014), 20120509, doi: 10.1098/rsta.2012.0509

(with Z. Rudnick) "On the eigenvalue spacing distribution for a point scatterer on the flat torus", arXiv, Ann. H. Poincaré 15 (2014), No. 1, 1-27, doi: 10.1007/s00023-013-0241-0

"The trace formula for a point scatterer on hyperbolic surfaces with one cusp", 34 pp., arXiv

(with Z. Rudnick) "Statistics of wave functions for a point scatterer on the torus", arXiv, Comm. Math. Phys. 316 (2012), No. 3, 763-782, doi: 10.1007/s00220-012-1556-2

"The trace formula for a point scatterer on a compact hyperbolic surface", 24 pp., arXiv, J. Math. Phys. 53 (2012), 012108, doi: 10.1063/1.3679761

"A counterexample to QUE", Oberwolfach Reports 49 (2011) on Quantum Ergodicity, 2825-28, doi: 10.4171/OWR/2011/49

Neuroscience

(with D. Trübutschek, S. Marti and S. Dehaene), "Probing the limits of activity-silent non-conscious working memory", Proc. Natl. Acad. Sc. (2019), 201820730; DOI:10.1073/pnas.1820730116

Theses:

"Spectral Properties of Intermediate Quantum Systems", 48 pp., HDR Thesis, Dept. of Mathematics, Sorbonne Université, October 2021.

"Quantum Chaos for point scatterers on hyperbolic surfaces", 113 pp., PhD Thesis, Dept. of Mathematics, University of Bristol, January 2011.