Aidan Backus

activity

20192023

collaborators

4 papers

math.DG2023

Regularity of sets of least perimeter in Riemannian manifolds

Aidan Backus

We give a short proof, in the tradition of the classical work of de Giorgi and Miranda on flat space, that the reduced boundary of a set of least perimeter in a Riemannian manifold…

math.CA2023

The fractal uncertainty principle via Dolgopyat's method in higher dimensions

Aidan Backus, James Leng, Zhongkai Tao

We prove a fractal uncertainty principle with exponent $\frac{d}{2} - δ + ε$ , $ε > 0$ , for Ahlfors--David regular subsets of $R^{d}$ with dimension $δ$ whi…

math.AP2020

The Breit-Wigner series for noncompactly supported potentials on the line

Aidan Backus

We propose a conjecture stating that for resonances, $λ_{j}$ , of a noncompactly supported potential, the series $\sum_{j} Im λ_{j} /∣ λ_{j} ∣^{2}$ diverges. This series appears i…

math.RA2019

An algorithm for computing root multiplicities in Kac-Moody algebras

Aidan Backus, Peter Connick, Joshua Lin

Root multiplicities encode information about the structure of Kac-Moody algebras, and appear in applications as far-reaching as string theory and the theory of modular functions. W…