# Bonjour—

### Finite-boundary element coupling in MATLAB

February 12, 2023

In this post, I talk about coupling the finite and boundary element methods for solving wave propagation problems in an inhomogeneous medium.

### Image matting with examples in Python

December 30, 2022

In this post, I talk about image and video matting—the process of extracting specific objects from an image to place them in a scene of a movie or compose them onto another background.

### The linear sampling method for random sources

November 4, 2022

In this post, I talk about an extension of the linear sampling method for solving the sound-soft inverse acoustic scattering problem with randomly distributed point sources.

### Singular integrals over curved elements

November 25, 2021

In this post, I talk about a new method for computing weakly singular and near-singular integrals that arise when solving the 3D Helmholtz equation with curved boundary elements.

### Quantum computing 4

December 6, 2020

Final episode of my series on quantum computing—in this post, I talk about quantum computing for supervised learning.

### Quantum computing 3

November 28, 2020

Episode 3 of my series on quantum computing—in this post, I talk about quantum computing for solving nonlinear ordinary differential equations.

### Quantum computing 2

November 17, 2020

Episode 2 of my series on quantum computing—in this post, I talk about the Schrödinger equation and quantum logic gates, which are the building blocks of quantum circuits and quantum computers.

### Quantum computing 1

November 11, 2020

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 Noether's theorem, which links symmetries (e.g., time invariance) to conserved quantities (e.g., energy)—this was a decisive moment in my life.

### Chloroquine & COVID-19 (in French)

October 25, 2020

Depuis mon retour en France, un sujet de conversation récurrent est bien évidemment la pandémie de la Covid-19. Et là, grosse surprise : beaucoup de gens autour de moi pensent toujours que l'hydroxychloroquine 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.

### Exponential integrators for stiff PDEs

May 19, 2020

One of the papers I wrote during my Ph.D. at Oxford was just accepted in Mathematics and Computers in Simulation. In this post, I review the main ideas of the paper.

### The U.K. government's controversial plan of action

March 19, 2020

I've been paying careful attention to the various government policies implemented in response to the coronavirus pandemic. Having many friends and colleagues in the U.K., I am particularly concerned with the British government's plan of action.

### Deep networks and the Kolmogorov–Arnold theorem

June 25, 2019

In my latest paper, my colleague and I prove a theorem about the approximation of multivariate functions by deep ReLU networks, for which the curse of dimensionality is lessened.

### Deep networks and bandlimited functions

March 2, 2019

In a recent paper, my colleagues and I considered the deep ReLU network approximation of generalized bandlimited functions.

### Computer-assisted proofs for PDEs

December 5, 2018

A couple of weeks ago, I spent a few days at McGill University with Jean-Philippe Lessard. He introduced me to the world of computer-assisted proofs, which I briefly describe in this post.

### Spherical caps in cell polarization

February 27, 2018

I have just submitted a paper about the modeling of embryogenesis with the Shvartsman group at Princeton University. Let me review the main ideas of our work.

### Solving nonlocal PDEs on the sphere

January 25, 2018

I have just submitted a paper about nonlocal PDEs on the sphere with my colleagues Mikael Slevinsky and Qiang Du. Here are the main ideas of our work.

### Gibbs phenomenon and Cesàro mean

January 4, 2018

In this post, I talk about a fascinating subject: the convergence of Fourier series and the Gibbs phenomenon.

### Deep networks and the curse of dimensionality

December 22, 2017

I started working on deep learning models when I began my research at Columbia University in September 2017. Coming from the approximation theory world, I wanted to learn about their approximation properties. A few months down the road I have proven a new theorem concerning the approximation of multivariate functions by deep ReLU networks.

### Solving PDEs on the sphere

October 26, 2017

My latest paper, with my former colleague Yuji Nakatsukasa, has just been accepted in SISC. In this post, I review the main ideas of our work.

### When planets dance

October 9, 2017

My second paper as a Ph.D. student, in collaboration with my friend and former colleague at Oxford Nikola Gushterov, was about the choreographies of the $$n$$-body problem. 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., these animations.