3 citations · 4 across the 5 of their papers we have counts for
8 papers
Planar Dirichlet eigenvalue bounds from a trace identity
Romain Speciel
We prove an asymptotically sharp lower bound for the eigenvalues of the Dirichlet Laplacian on bounded open sets in the plane with area . The proof employs a trace ident…
An inverse problem on eigenfunction triple products
Carl Schildkraut, Romain Speciel
On a connected closed smooth Riemannian manifold, the algebraic structure of the Laplace eigenfunctions, as described by eigenfunction triple products, uniquely determines the geom…
Geometric rigidity from the Dirichlet-to-Neumann operator
Romain Speciel
The analytic properties of the Dirichlet-to-Neumann operator reflect the geometry of the underlying manifold. As a guiding example of this relationship, consider the Euclidean unit…
Stability Estimates for Commutativity Properties of the Dirichlet-to-Neumann Operator
Romain Speciel
The Laplacian on the unit sphere has the property that it can explicitly be expressed in terms of , the Dirichlet-t…
A Deformation Approach to the BFK Formula
Romain Speciel
Understanding how spectral quantities localize on manifolds is a central theme in geometric spectral theory and index theory. Within this framework, the BFK formula, obtained by Bu…
Surfaces with Commuting Boundary Laplacian and Dirichlet-to-Neumann Map
Romain Speciel
For a smooth, connected, compact -dimensional submanifold with boundary, equipped with the standard metric, the Laplacian on is know…
Continuous limits of generalized pentagram maps
Danny Nackan, Romain Speciel
We provide a rigorous treatment of continuous limits for various generalizations of the pentagram map on polygons in by means of quantum calculus. Describing this l…
Evaluating Ensemble Robustness Against Adversarial Attacks
George Adam, Romain Speciel
Adversarial examples, which are slightly perturbed inputs generated with the aim of fooling a neural network, are known to transfer between models; adversaries which are effective…