Jesse Gell-Redman

Deep Learning Is Singular, and That's Good

Susan Wei, Daniel Murfet, Mingming Gong, Hui Li, Jesse Gell-Redman, Thomas Quella

Journal article  |  2022  |  IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS

In singular models, the optimal set of parameters forms an analytic set with singularities, and a classical statistical inference ..

The Distribution of Phase Shifts for Semiclassical Potentials with Polynomial Decay

Jesse Gell-Redman, Andrew Hassell

Journal article  |  2020  |  INTERNATIONAL MATHEMATICS RESEARCH NOTICES

This is the 3rd paper in a series [6, 9] analyzing the asymptotic distribution of the phase shifts in the semiclassical limit. We ..

EXISTENCE AND ASYMPTOTICS OF NONLINEAR HELMHOLTZ EIGENFUNCTIONS

Jesse Gell-Redman, Andrew Hassell, Jacob Shapiro, Junyong Zhang

Journal article  |  2020  |  SIAM JOURNAL ON MATHEMATICAL ANALYSIS

We prove the existence and asymptotic expansion of a large class of solutions to nonlinear Helmholtz equations of the form (Δ-λ2)u..

Equidistribution of phase shifts in obstacle scattering

Jesse Gell-Redman, Maxime Ingremeau

Journal article  |  2019  |  COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS

For scattering off a smooth, strictly convex obstacle (Formula presented.) with positive curvature, we show that the eigenvalues o..

Spectral and Hodge theory of "Witt" incomplete cusp edge spaces

Jesse Gell-Redman, Jan Swoboda

Journal article  |  2019  |  COMMENTARII MATHEMATICI HELVETICI

Incomplete cusp edges model the behavior of the Weil-Petersson metric on the compactified Riemann moduli space near the interior o..

The Feynman Propagator on Perturbations of Minkowski Space

Jesse Gell-Redman, Nick Haber, Andras Vasy

Journal article  |  2016  |  COMMUNICATIONS IN MATHEMATICAL PHYSICS

In this paper we analyze the Feynman wave equation on Lorentzian scattering spaces. We prove that the Feynman propagator exists as..

The Index of Dirac Operators on Incomplete Edge Spaces

Pierre Albin, Jesse Gell-Redman

Journal article  |  2016  |  SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS

We derive a formula for the index of a Dirac operator on a compact, evendimensional incomplete edge space satisfying a “geometric ..

Harmonic maps of conic surfaces with cone angles less than 2 pi

Jesse Gell-Redman

Journal article  |  2015  |  COMMUNICATIONS IN ANALYSIS AND GEOMETRY

We prove the existence and uniqueness of harmonic maps in degree one homotopy classes of closed, orientable surfaces of positive g..

Hodge cohomology of some foliated boundary and foliated cusp metrics

Jesse Gell-Redman, Frederic Rochon

Journal article  |  2015  |  MATHEMATISCHE NACHRICHTEN

For fibred boundary and fibred cusp metrics, Hausel, Hunsicker, and Mazzeo identified the space of L2 harmonic forms of fixed degr..

Equidistribution of phase shifts in semiclassical potential scattering

Jesse Gell-Redman, Andrew Hassell, Steve Zelditch

Journal article  |  2015  |  JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES

Consider the Hamiltonian H:= h2 Δ +V-E where Δ is the positive Laplacian on Rd, V in C0(Rd) is a smooth, compactly supported poten..