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<!DOCTYPE html>
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<h1>Bonjour—</h1>
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<h3><a href="2024-02-04.html">The linear sampling method for small random scatterers</a></h3>
</div>
<div class="blog-post-format">
<span><i class="fa fa-date"></i>February 4, 2024</span>
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<div class="blog-post-des">
<p>In this post, I talk about an extension of the linear sampling method for solving the sound-soft <a href="https://en.wikipedia.org/wiki/Inverse_scattering_problem">inverse acoustic scattering</a> problem with data generated by randomly distributed small <a href="https://en.wikipedia.org/wiki/Scattering">scatterers</a>.</p>
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<h3><a href="2023-10-02.html">Strongly singular integrals over curved elements</a></h3>
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<span><i class="fa fa-date"></i>October 2, 2023</span>
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<div class="blog-post-des">
<p>In this post, I talk about a new method for computing strongly singular and near-singular integrals that arise when solving the 3D <a href="https://en.wikipedia.org/wiki/Helmholtz_equation">Helmholtz equation</a> with curved <a href="https://en.wikipedia.org/wiki/Boundary_element_method">boundary elements</a>.</p>
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<h3><a href="2023-02-12.html">Finite-boundary element coupling in MATLAB</a></h3>
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<span><i class="fa fa-date"></i>February 12, 2023</span>
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<div class="blog-post-des">
<p>In this post, I talk about coupling the finite and boundary element methods for solving <a href="https://en.wikipedia.org/wiki/Wave_propagation">wave propagation</a> problems in an inhomogeneous medium.</p>
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<h3><a href="2022-12-30.html">Image matting with examples in Python</a></h3>
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<span><i class="fa fa-date"></i> December 30, 2022</span>
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<div class="blog-post-des">
<p>In this post, I talk about image and video <a href="https://en.wikipedia.org/wiki/Video_matting">matting</a>—the process of extracting specific objects from an image to place them in a scene of a movie or compose them onto another background.</p>
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<h3><a href="2022-11-04.html">The linear sampling method for random sources</a></h3>
</div>
<div class="blog-post-format">
<span><i class="fa fa-date"></i> November 4, 2022</span>
</div>
<div class="blog-post-des">
<p>In this post, I talk about an extension of the linear sampling method for solving the sound-soft <a href="https://en.wikipedia.org/wiki/Inverse_scattering_problem">inverse acoustic scattering</a> problem with randomly distributed point sources.</p>
<a href="2022-11-04.html" class="btn btn-default">Continue Reading</a>
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<h3><a href="2021-11-25.html">Weakly singular integrals over curved elements</a></h3>
</div>
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<span><i class="fa fa-date"></i> November 25, 2021</span>
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<div class="blog-post-des">
<p>In this post, I talk about a new method for computing weakly singular and near-singular integrals that arise when solving the 3D <a href="https://en.wikipedia.org/wiki/Helmholtz_equation">Helmholtz equation</a> with curved <a href="https://en.wikipedia.org/wiki/Boundary_element_method">boundary elements</a>.</p>
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<h3><a href="2020-12-06.html">Quantum computing 4</a></h3>
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<span><i class="fa fa-date"></i> December 6, 2020</span>
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<div class="blog-post-des">
<p>Final episode of my series on quantum computing—in this post, I talk about quantum computing for <a href='https://en.wikipedia.org/wiki/Supervised_learning'>supervised learning</a>.</p>
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<h3><a href="2020-11-28.html">Quantum computing 3</a></h3>
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<div class="blog-post-format">
<span><i class="fa fa-date"></i> November 28, 2020</span>
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<div class="blog-post-des">
<p>Episode 3 of my series on quantum computing—in this post, I talk about quantum computing for solving nonlinear <a href='https://en.wikipedia.org/wiki/Ordinary_differential_equation'>ordinary differential equations</a>.</p>
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<h3><a href="2020-11-17.html">Quantum computing 2</a></h3>
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<span><i class="fa fa-date"></i> November 17, 2020</span>
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<div class="blog-post-des">
<p>Episode 2 of my series on quantum computing—in this post, I talk about the <a href='https://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation'>Schrödinger equation</a> and <a href='https://en.wikipedia.org/wiki/Quantum_logic_gate'>quantum logic gates</a>, which are the building blocks of <a href='https://en.wikipedia.org/wiki/Quantum_circuit#:~:text=In%20quantum%20information%20theory%2C%20a,as%20an%20n%2Dqubit%20register.'>quantum circuits</a> and <a href='https://en.wikipedia.org/wiki/Quantum_computing'>quantum computers</a>.</p>
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<h3><a href="2020-11-11.html">Quantum computing 1</a></h3>
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<span><i class="fa fa-date"></i> November 11, 2020</span>
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<div class="blog-post-des">
<p>In my first research project as an undergraduate student in the summer of 2010, I worked on groups and symmetries in classical and quantum physics. One day in the library I came across <a href='https://en.wikipedia.org/wiki/Noether%27s_theorem'>Noether's theorem</a>, which links symmetries (e.g., time invariance) to conserved quantities (e.g., energy)—this was a decisive moment in my life.</p>
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<h3><a href="2020-10-25.html">Chloroquine & COVID-19 (in French)</a></h3>
</div>
<div class="blog-post-format">
<span><i class="fa fa-date"></i> October 25, 2020</span>
</div>
<div class="blog-post-des">
<p>Depuis mon retour en France, un sujet de conversation récurrent est bien évidemment la pandémie de la <a href='https://fr.wikipedia.org/wiki/Pand%C3%A9mie_de_Covid-19'> Covid-19</a>. Et là, grosse surprise : beaucoup de gens autour de moi pensent toujours que <a href='https://fr.wikipedia.org/wiki/Hydroxychloroquine'>l'hydroxychloroquine</a> est, ou pourrait être, un médicament efficace contre la Covid-19. Ce qui est surprenant, c'est qu'aux États-Unis, la folie derrière l'hydroxychloroquine est terminée ! Mais pas en France.</p>
<a href="2020-10-25.html" class="btn btn-default">Continue Reading</a>
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<div class="blog-post-thumb">
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<h3><a href="2020-05-19.html">Exponential integrators for stiff PDEs</a></h3>
</div>
<div class="blog-post-format">
<span><i class="fa fa-date"></i> May 19, 2020</span>
</div>
<div class="blog-post-des">
<p><a href="https://arxiv.org/pdf/1604.08900.pdf">One of the papers</a> I wrote during my Ph.D. at Oxford was just accepted in <a href="https://www.journals.elsevier.com/mathematics-and-computers-in-simulation">Mathematics and Computers in Simulation</a>. In this post, I review the main ideas of the paper.</p>
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</div>
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<div class="blog-post-title">
<h3><a href="2020-03-19.html">The U.K. government's controversial plan of action</a></h3>
</div>
<div class="blog-post-format">
<span><i class="fa fa-date"></i> March 19, 2020</span>
</div>
<div class="blog-post-des">
<p>I've been paying careful attention to the various government policies implemented in response to the <a href='https://en.wikipedia.org/wiki/2019%E2%80%9320_coronavirus_pandemic'>coronavirus pandemic</a>. Having many friends and colleagues in the U.K., I am particularly concerned with the <a href='https://www.gov.uk/government/publications/coronavirus-action-plan'>British government's plan of action</a>.</p>
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</div>
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<div class="blog-post-thumb">
<div class="blog-post-title">
<h3><a href="2019-06-25.html">Deep networks and the Kolmogorov–Arnold theorem</a></h3>
</div>
<div class="blog-post-format">
<span><i class="fa fa-date"></i> June 25, 2019</span>
</div>
<div class="blog-post-des">
<p>In my latest <a href="https://arxiv.org/pdf/1906.11945.pdf">paper</a>, my colleague and I prove a theorem about the <a href='https://en.wikipedia.org/wiki/Approximation_theory'>approximation</a> of <a href='https://en.wikipedia.org/wiki/Function_of_several_real_variables'>multivariate</a> functions by <a href='https://en.wikipedia.org/wiki/Deep_learning'>deep ReLU networks</a>, for which the <a href='https://en.wikipedia.org/wiki/Curse_of_dimensionality'>curse of dimensionality</a> is lessened.</p>
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<div class="blog-post-thumb">
<div class="blog-post-title">
<h3><a href="2019-03-02.html">Deep networks and bandlimited functions</a></h3>
</div>
<div class="blog-post-format">
<span><i class="fa fa-date"></i> March 2, 2019</span>
</div>
<div class="blog-post-des">
<p>In a recent <a href="https://arxiv.org/pdf/1903.00735.pdf">paper</a>, my colleagues and I considered the <a href='https://en.wikipedia.org/wiki/Deep_learning'>deep</a> <a href='https://en.wikipedia.org/wiki/Rectifier_(neural_networks)'>ReLU</a> network approximation of generalized <a href='https://en.wikipedia.org/wiki/Bandlimiting'>bandlimited</a> functions.</p>
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</div>
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<div class="blog-post-thumb">
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<h3><a href="2018-12-05.html">Computer-assisted proofs for PDEs</a></h3>
</div>
<div class="blog-post-format">
<span><i class="fa fa-date"></i> December 5, 2018</span>
</div>
<div class="blog-post-des">
<p>A couple of weeks ago, I spent a few days at
<a href="https://mcgill.ca/">McGill University</a>
with <a href="https://www.math.mcgill.ca/jplessard/Home.html">Jean-Philippe Lessard</a>.
He introduced me to the world of <a href="https://en.wikipedia.org/wiki/Computer-assisted_proof">computer-assisted proofs</a>, which I briefly describe in this post.</p>
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</div>
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<div class="blog-post-thumb">
<div class="blog-post-title">
<h3><a href="2018-02-27.html">Spherical caps in cell polarization</a></h3>
</div>
<div class="blog-post-format">
<span><i class="fa fa-date"></i> February 27, 2018</span>
</div>
<div class="blog-post-des">
<p>I have just submitted a <a href="https://www.cell.com/biophysj/fulltext/S0006-3495(18)30672-6">paper</a> about the modeling of
<a href="https://en.wikipedia.org/wiki/Embryogenesis">embryogenesis</a> with the
<a href="https://shvartsmanlab.com">Shvartsman group</a> at
<a href="https://www.princeton.edu">Princeton University</a>.
Let me review the main ideas of our work.</p>
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</div>
</div>
<div class="blog-post-thumb">
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<h3><a href="2018-01-25.html">Solving nonlocal PDEs on the sphere</a></h3>
</div>
<div class="blog-post-format">
<span><i class="fa fa-date"></i> January 25, 2018</span>
</div>
<div class="blog-post-des">
<p>I have just submitted <a href="https://arxiv.org/pdf/1801.04902.pdf">a paper</a> about <a href="https://www.ma.utexas.edu/mediawiki/index.php/Introduction_to_nonlocal_equations">nonlocal PDEs</a>
on the sphere with my colleagues
<a href="https://home.cc.umanitoba.ca/~slevinrm/">Mikael Slevinsky</a> and
<a href="https://www.columbia.edu/~qd2125/">Qiang Du</a>.
Here are the main ideas of our work.</p>
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</div>
</div>
<div class="blog-post-thumb">
<div class="blog-post-title">
<h3><a href="2018-01-04.html">Gibbs phenomenon and Cesàro mean</a></h3>
</div>
<div class="blog-post-format">
<span><i class="fa fa-date"></i> January 4, 2018</span>
</div>
<div class="blog-post-des">
<p>In this post, I talk about a fascinating subject: the
<a href="https://en.wikipedia.org/wiki/Convergence_of_Fourier_series#Uniform_convergence">convergence of Fourier series</a> and the
<a href="https://en.wikipedia.org/wiki/Gibbs_phenomenon">Gibbs phenomenon</a>.</p>
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</div>
</div>
<div class="blog-post-thumb">
<div class="blog-post-title">
<h3><a href="2017-12-22.html">Deep networks and the curse of dimensionality</a></h3>
</div>
<div class="blog-post-format">
<span><i class="fa fa-date"></i> December 22, 2017</span>
</div>
<div class="blog-post-des">
<p>I started working on <a href="https://en.wikipedia.org/wiki/Deep_learning">deep learning</a>
models when I began my research at <a href="http//www.columbia.edu">Columbia University</a> in September 2017. Coming from the <a href="https://en.wikipedia.org/wiki/Approximation_theory">approximation theory</a> world, I wanted to learn about their approximation properties. A few months down the road I have proven a <a href="https://arxiv.org/pdf/1712.08688.pdf">new theorem</a> concerning the approximation of
<a href="https://en.wikipedia.org/wiki/Function_of_several_real_variables">multivariate functions</a> by deep ReLU networks.</p>
<a href="2017-12-22.html" class="btn btn-default">Continue Reading</a>
</div>
</div>
<div class="blog-post-thumb">
<div class="blog-post-title">
<h3><a href="2017-10-26.html">Solving PDEs on the sphere</a></h3>
</div>
<div class="blog-post-format">
<span><i class="fa fa-date"></i> October 26, 2017</span>
</div>
<div class="blog-post-des">
<p><a href="https://arxiv.org/pdf/1701.06030.pdf">My latest paper</a>, with my former colleague
<a href="https://www.opt.mist.i.u-tokyo.ac.jp/~nakatsukasa/">Yuji Nakatsukasa</a>, has just been accepted in
<a href="https://www.siam.org/journals/sisc.php">SISC</a>. In this post, I review the main ideas of our work.</p>
<a href="2017-10-26.html" class="btn btn-default">Continue Reading</a>
</div>
</div>
<div class="blog-post-thumb">
<div class="blog-post-title">
<h3><a href="2017-10-09.html">When planets dance</a></h3>
</div>
<div class="blog-post-format">
<span><i class="fa fa-date"></i> October 9, 2017</span>
</div>
<div class="blog-post-des">
<p><a href="https://epubs.siam.org/doi/abs/10.1137/15M1024652">My second paper</a> as a Ph.D. student,
in collaboration with my friend and former colleague at Oxford <a href="https://scholar.google.com/citations?user=w-PVG8sAAAAJ&hl=en">Nikola Gushterov</a>,
was about the <a href="https://www.scholarpedia.org/article/N-body_choreographies">choreographies</a>
of the <a href="https://en.wikipedia.org/wiki/N-body_problem">\(n\)-body problem</a>.
These are very simple periodic solutions of the \(n\)-body problem, in which the bodies share a common orbit and are uniformly spread along it; see, e.g., <a href="https://personalpages.manchester.ac.uk/staff/j.montaldi/Choreographies/">these animations</a>.</p>
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