![Me](photopetit.jpg) I'm a "professeur junior" (CPJ) at the Laboratoire de Mathématiques d'Orsay, Université Paris-Saclay (bureau 2G1). Before Nov 2022, I was a researcher (CR) at Inria Paris, in the MATHERIALS project-team, located at CERMICS, Ecole des Ponts. ## Research interests Development and analysis of numerical methods in quantum chemistry and materials science ## Publications #### Preprints * É. Cancès, F. Faulstich, A. Kirsch, É. Letournel, A. Levitt, Some mathematical insights on Density Matrix Embedding Theory (2023), [preprint](https://arxiv.org/abs/2305.16472) #### Published or accepted * É. Cancès, G. Kemlin, A. Levitt, A priori error analysis of linear and nonlinear periodic Schrödinger equations with analytic potentials, Journal of Scientific Computing (2023), [preprint](https://hal.inria.fr/hal-03692851) * T. Nottoli, I. Giannı̀, A. Levitt, F. Lipparini, A robust, open-source implementation of the locally optimal block preconditioned conjugate gradient for large eigenvalue problems in quantum chemistry, Theoretical Chemistry Accounts (2023), [preprint](https://hal.science/hal-04094087) * I. Duchemin, A. Levitt, Computing photoionization spectra in Gaussian basis sets, Journal of Chemical Physics (2023), [preprint](https://inria.hal.science/hal-04100359) * É. Cancès, A. Levitt, Y. Maday, C. Yang, Numerical Methods for Kohn–Sham Models: Discretization, Algorithms, and Error Analysis, book chapter, [link](https://link.springer.com/book/10.1007/978-3-031-22340-2) * É. Cancès, M. Herbst, G. Kemlin, A. Levitt, B. Stamm, Numerical stability and efficiency of response property calculations in density functional theory, Letters in Mathematical Physics (2023), [preprint](https://arxiv.org/abs/2210.04512) * J. Toulouse, K. Schwinn, F. Zapata, A. Levitt, É. Cancès, E. Luppi, Photoionization and core resonances from range-separated time-dependent density-functional theory for open-shell states: Example of the lithium atom, Journal of Chemical Physics (2022), [preprint](https://hal.sorbonne-universite.fr/hal-03849878) * A. Castellano, F. Bottin, J. Bouchet, A. Levitt, G. Stoltz, Ab initio Canonical Sampling based on Variational Inference, Physical Review B letter (2022), [preprint](https://arxiv.org/abs/2210.11531) * É. Cancès, G. Dusson, G. Kemlin, A. Levitt, Practical error bounds for properties in plane-wave electronic structure calculations, SIAM Journal on Scientific Computing (2022), [preprint](https://hal.inria.fr/hal-03408321) * I. Duchemin, L. Genovese, E. Letournel, A. Levitt, S. Ruget, Efficient extraction of resonant states in systems with defects, Journal of Computational Physics (2022), [preprint](https://hal.archives-ouvertes.fr/hal-03611185/document) * K. Schwinn, F. Zapata, A. Levitt, É. Cancès, E. Luppi, J. Toulouse, Photoionization and core resonances from range-separated density-functional theory: General formalism and example of the beryllium atom, Journal of Chemical Physics (2022), [preprint](https://hal.sorbonne-universite.fr/hal-03605574/document) * M. Herbst, A. Levitt, A robust and efficient line search for self-consistent field iterations, Journal of Computational Physics (2021), [preprint](https://arxiv.org/abs/2109.14018) * M-S. Dupuy, A. Levitt, Finite-size effects in response functions of molecular systems, SMAI Journal of Computational Mathematics (2021), [preprint](https://arxiv.org/abs/2102.09841) * E. Bernard, M. Fathi, A. Levitt, G. Stoltz, Hypocoercivity with Schur complements, Annales Henri Lebesgue (2021), [preprint](https://arxiv.org/abs/2003.00726) * É. Cancès, C. Fermanian Kammerer, A. Levitt, S. Siraj-Dine, Coherent electronic transport in periodic crystals, Annales Henri Poincaré (2021), [preprint](https://arxiv.org/abs/2002.01990) * É. Cancès, G. Kemlin, A. Levitt, Convergence analysis of direct minimization and self-consistent iterations, SIAM Journal on Matrix Analysis and Applications (2021), [preprint](https://arxiv.org/abs/2004.09088) * M. Herbst, A. Levitt, Black-box inhomogeneous preconditioning for self-consistent field iterations in density functional theory, Journal of Physics: Condensed Matter (2020), [preprint](https://arxiv.org/abs/2009.01665) * A. Levitt, Screening in the finite-temperature reduced Hartree-Fock model, Archive for Rational Mechanics and Analysis (2020), [preprint](https://arxiv.org/abs/1810.03342) * M. Herbst, A. Levitt, É. Cancès, A posteriori error estimation for the non-self-consistent Kohn-Sham equations, Faraday Discussions (2020), [preprint](https://arxiv.org/abs/2004.13549) * É. Cancès, V. Ehrlacher, D. Gontier, A. Levitt, D. Lombardi, Numerical quadrature in the Brillouin zone for periodic Schrodinger operators, Numerische Mathematik (2019), [preprint](https://arxiv.org/abs/1805.07144) * D. Gontier, A. Levitt, S. Siraj-Dine, Numerical construction of Wannier functions through homotopy, Journal of Mathematical Physics (2019), [preprint](https://arxiv.org/abs/1812.06746) * A. Damle, A. Levitt, L. Lin, Variational formulation for Wannier functions with entangled band structure, SIAM MMS (2019), [preprint](https://arxiv.org/abs/1801.08572) * H. Cornean, D. Gontier, A. Levitt, D. Monaco, Localised Wannier functions in metallic systems, Annales Henri Poincaré (2019), [preprint](https://arxiv.org/abs/1712.07954) * A. Levitt, C. Ortner, Convergence and Cycling in Walker-type Saddle Search Algorithms, SIAM Journal on Numerical Analysis (2017), [preprint](http://arxiv.org/abs/1607.08875) * X. Antoine, A. Levitt, Q. Tang, Efficient spectral computation of the stationary states of rotating Bose-Einstein condensates by the preconditioned nonlinear conjugate gradient method, Journal of Computational Physics 343 (2017), [preprint](https://arxiv.org/abs/1611.02045) * É. Cancès, A. Levitt, G. Panati, G. Stoltz, Robust determination of maximally-localized Wannier functions, Phys. Rev. B, 95, 075114 (2017), [preprint](http://arxiv.org/abs/1605.07201) * F. Aviat, A. Levitt, et. al., Truncated Conjugate Gradient (TCG): an optimal strategy for the analytical evaluation of the many-body polarization energy and forces in molecular simulations, J. Chem. Theory Comput., 13 (1), pp 180–190 (2017), [preprint](https://hal.archives-ouvertes.fr/hal-01395833/) * X. Gonze, F. Jollet et al., Recent developments in the ABINIT software package. Computer Physics Communications, 205:106-131 (2016), [journal](http://www.sciencedirect.com/science/article/pii/S0010465516300923) * A. Levitt, M. Torrent, Parallel eigensolvers in plane-wave Density Functional Theory. Computer Physics Communications, 187:98–105 (2015), [preprint](http://arxiv.org/abs/1406.4350) * A. Levitt, Solutions of the multiconfiguration Dirac-Fock equations. Reviews in Mathematical Physics, 26(07):1450014 (2014), [preprint](http://arxiv.org/abs/1305.3739) * A. Levitt, Best constants in Lieb-Thirring inequalities: a numerical investigation. Journal of Spectral Theory 4.1 (2014), [preprint](http://arxiv.org/abs/1206.1473) * A. Levitt, Convergence of gradient-based algorithms for the Hartree-Fock equations. ESAIM Math. Model. Numer. Anal. 46.06 (2012), [preprint](http://arxiv.org/abs/1109.5473/) * G. James, A. Levitt, C. Ferreira, Continuation of discrete breathers from infinity in a nonlinear model for DNA breathing. Applicable Analysis 89.9 (2010), [preprint](jlf.pdf) ## Teaching materials * 2024 [Calcul scientifique](MAO.pdf), M1 * 2023 [Mathematical methods in quantum mechanics](MMQM), M2 * 2021 [Introduction to functional analysis](OMPI.pdf), L3 * 2021 [Practical scientific computing](calsci.pdf), L3 * 2019 Mini-course: [Complex analysis for quantum physicists and chemists](complex_analysis.pdf) * 2016- [Analyse de Fourier](fourier), M1 ## Notes These are unreviewed notes on basic techniques that I made for my own usage and that may (or may not) be helpful and/or correct. Use at your own risk and please report any mistakes or omissions. * 2023 [Van der Waals interactions from first principles](dispersion.pdf) * 2022 [What is the response function of an oscillatory system?](response_oscillatory.pdf) * 2021 [The many disguises of the Schur complement](schur.pdf) * 2020 [The adjoint trick and automatic differentiation](adjoint.pdf) * 2019 [Ewald summation](ewald.pdf) ## Talks Slides of selected talks at conferences or seminars that may or may not be clearer than papers. Again, no warranty. * 2023 Review on numerical methods for quantum dynamics, Italian maths of QM online seminar, [link](talks/italy.pdf) * 2022 Response functions and resonances, Collège de France, [link](talks/collegedefrance.pdf) * 2021 Direct minimization vs SCF for nonlinear eigenspace problems, SIAM linear algebra, [link](talks/SIAM_LA.pdf) * 2020 Numerical analysis and properties of crystals, internal MATHERIALS seminar, [link](talks/MATHERIALS.pdf) * 2020 HDR defence [link](talks/HDR.pdf) * 2019 Screening and charge sloshing in crystals, ICIAM minisymposium [link](talks/ICIAM.pdf) * 2019 Wannier functions for insulators and metals, Copenhagen [link](talks/copenhagen.pdf) * 2018 Numerical integration in the Brillouin zone, Beijing [link](talks/beijing.pdf) ## Software * [DFTK.jl](https://github.com/mfherbst/DFTK.jl), the density functional toolkit * Computation of [Wannier functions](https://github.com/antoine-levitt/wannier) ## Misc links * (very out of date...) [resume](cv.pdf) * [HDR thesis](hdr.pdf) and [PhD thesis](https://hal.archives-ouvertes.fr/tel-00881031) ## Contact antoine (dot) levitt (at) universite-paris-saclay (dot) fr