Simon St-Amant

We study the broken non-abelian X-ray transform in Minkowski space. This transform acts on the space of Hermitian connections on a causal diamond and is known to be injective up to an infinite-dimensional gauge. We show a stability estimate that takes into account the gauge, leading to a new proof of the transform's injectivity. Our proof leads us...

We study the broken non-abelian X-ray transform in Minkowski space. This transform acts on the space of Hermitian connections on a causal diamond and is known to be injective up to an infinite-dimensional gauge. We show a stability estimate that takes into account the gauge, leading to a new proof of the transform's injectivity. Our proof leads us...

We consider the three-dimensional sloshing problem on a triangular prism whose angles with the sloshing surface are of the form ${\pi}/{2q}$ , where q is an integer. We are interested in finding a two-term asymptotic expansion of the eigenvalue counting function. When both angles are ${\pi}/{4}$ , we compute the exact value of the second term. As f...

We obtain a complete asymptotic expansion for the eigenvalues of the Dirichlet-to-Neumann maps associated with Schrödinger operators on Riemannian surfaces with boundary. For the zero potential, we recover the well-known spectral asymptotics for the Steklov problem. For non-zero potentials, we obtain new geometric invariants determined by the spect...

We investigate random compact sets with random functions defined thereon, such as polynomials, rational functions, the pluricomplex Green function and the Siciak extremal function. One surprising consequence of our study is that randomness can be used to `improve' convergence for sequences of functions.

We consider the three-dimensional sloshing problem on a triangular prism whose angles with the sloshing surface are of the form $\frac{\pi}{2q}$, where $q$ is an integer. We are interested in finding a two-term asymptotic expansion of the eigenvalue counting function. When both angles are $\frac{\pi}{4}$, we compute the exact value of the second te...

We obtain a complete asymptotic expansion for the eigenvalues of the Dirichlet-to-Neumann maps associated with Schr\"odinger operators on Riemannian surfaces with boundary. For the zero potential, we recover the well-known spectral asymptotics for the Steklov problem. For nonzero porentials, we obtain new geometric invariants determined by the spec...

We seek random versions of some classical theorems on complex approximation by polynomials and rational functions, as well as investigate properties of random compact sets in connection to complex approximation.

We seek random versions of some classical theorems on complex approximation by polynomials and rational functions, as well as investigate properties of random compact sets in connection to complex approximation.