Software
Papers
-2024 The linear sampling method for small random scatterers
+2023 The linear sampling method for random sources doi arXiv
Blog posts
-2024 The linear sampling method for small random scatterers
+2022 The linear sampling method for random sources
@@ -254,9 +254,7 @@
Software
Papers
2021 Deep ReLU networks overcome the curse of dimensionality for generalized bandlimited functions doi arXiv
-2020 Error bounds for deep ReLU networks using the Kolmogorov–Arnold superposition theorem doi arXiv
-2019 New error bounds for deep ReLU networks using sparse grids doi arXiv
Blog posts
@@ -275,7 +273,7 @@Background
These packages are particularly relevant to the astrophysics, computational fluid dynamics, and biology communities, where simple geometries such as the sphere are prevalent. For example, nonlinear advection equations on the sphere, such as the shallow water equations, are of significant importance in atmospheric numerical modeling, while reaction-diffusion equations in a spherical shell are widely used as a model for convection patterns within the Earth's mantle, as well as for the modeling of morphogenesis in embryos. On top of these standard local differential equations, their nonlocal integral analogs are becoming more and more popular to model a wide range of phenomena in these communities.
-Results (Ph.D. at Oxford)
+Results
My Ph.D. introduced new numerical methods for the simulation of periodic physical phenomena.
@@ -322,9 +320,7 @@Results (Ph.D. at Oxford)
- Results (Postdoc at Columbia)
- -With discretizations of operators in hand, I explored potential applications in biology. I used the fast algorithms I developed to investigate pattern formation and explain symmetry breaking on the sphere.
+With discretizations of operators in hand, I explored potential applications in biology during a postdoc at Columbia. I used the fast algorithms I developed to investigate pattern formation and explain symmetry breaking on the sphere.
@@ -341,7 +337,7 @@ Results (Postdoc at Columbia)
Several years later, in 2024, I introduced a nonlocal vector calculus on the sphere based on weakly singular integral operators. When employing scalar and vector spherical harmonics as bases, I showed that these nonlocal operators exhibit diagonal behavior. Through analysis, I also established strong convergence to the operators of local vector calculus as the interaction range approaches zero. This work is consistent with my previous work on nonlocal diffusion operators. This extends to the sphere, a prototype of a manifold, the nonlocal calculus for Euclidean domains.
+Collaborators
@@ -355,25 +351,18 @@Software
Papers
-2024 Nonlocal vector calculus on the sphere using vector spherical harmonics
- +2020 Solving periodic semilinear stiff PDEs in 1D, 2D and 3D with exponential integrators doi arXiv
-2018 Spherical caps in cell polarization doi
- -2018 A spectral method for nonlocal diffusion operators on the sphere doi arXiv
- +2018 A spectral method for nonlocal diffusion operators on the sphere doi arXiv
2018 Fourth-order time-stepping for stiff PDEs on the sphere doi arXiv
-2016 Computing hyperbolic choreographies doi arXiv
-2016 Computing planar and spherical choreographies doi arXiv
-2015 Extension of Chebfun to periodic functions doi arXiv
Blog posts
-2024 Nonlocal vector calculus on the sphere
+2020 Exponential integrators for stiff PDEs
2018 Computer-assisted proofs for PDEs
2018 Spherical caps in cell polarization
diff --git a/teaching.html b/teaching.html index b0dca3a..caa5097 100755 --- a/teaching.html +++ b/teaching.html @@ -102,10 +102,10 @@IP Paris
2023–2024
-Optimization & control (École Polytechnique)
+Optimization & Control (École Polytechnique)
Statistics (ENSTA Paris)
Probability (ENSTA Paris)
-Modelling & simulations (École Polytechnique)
+Modelling & Simulations (École Polytechnique)
Dynamical systems (ENSTA Paris)