Ethan W. Sussman

Current position: NSF Postdoctoral Fellow, Northwestern University

Email: "ethan.sussman" + U+0040 +"northwestern.edu"

Office: Lunt B23

About Me:

I am an analyst specializing in microlocal analysis and singular geometry and their applications to partial differential equations and mathematical physics more broadly. Previously, I was a Szego Assistant Professor at Stanford University. Before that, I did my PhD at MIT, where I was fortunate to be advised by Peter Hintz.

Education:

Ph.D. in Pure Mathematics, MIT, 2023.

B.Sc. in Mathematics and Physics, Stanford University, 2018.

Works in progress:

Microlocal analysis of the nonrelativistic limit of the Klein--Gordon equation. (Joint with Andrew Hassell, Qiuye Jia, Andras Vasy.)
The asymptotic structure of forward scattering. (Joint with Nick Lohr, Izak Oltman, and Joey Zhou.)
Convergence of the Born series for Coulombic potentials on asymptotically conic manifolds. (Joint with Jared Wunsch.)

Titles tentative. Click here for a live feed of me working on these manuscripts.

Teaching:

Stanford Math 173, Spring 2024: Theory of Partial Differential Equations
Stanford Math 21, Winter 2024: Calculus III
MIT 18.089, Summer 2021: Calculus for Naval Engineers.

A figure:

A statement:

I stand against antisemitism and other forms of fashionable prejudice. And for those suffering from internalized antisemitism: a reminder. Bundism saved no one.

Current topics of interest:

Wave propagation on manifolds, including both the Schrödinger equation and relativistic wave equations.
Scattering theory for repulsive Coulombic point scatterers.
Perturbed plane waves in potential scattering.

Publications and preprints:

The microlocal analysis of the non-relativistic limit of the Klein--Gordon equation: asymptotics, joint with Andrew Hassell, Qiuye Jia, and Andras Vasy.
In preparation.

The microlocal analysis of the non-relativistic limit of the Klein--Gordon equation: estimates, joint with Andrew Hassell, Qiuye Jia, and Andras Vasy.
In preparation.

The essential self-adjointness of the wave operator on radiative spacetimes, joint with Qiuye Jia and Mikhail Molodyk.
Preprint, 2024. arXiv:2412.03828 [math.SP].

Complete asymptotic analysis of low energy scattering for Schrödinger operators with a short-range potential.
Preprint, 2024. arXiv:2411.04220 [math.AP].

Asymptotics in all regimes for the Schrödinger equation with time-independent coefficients, joint with Shi-Zhuo Looi.
Preprint, 2024. arXiv:2407.20991 [math.AP].

Full semiclassical asymptotics near transition points.
Preprint, 2023. To appear in Pure and Applied Analysis (PAA). arXiv:2312.00965 [math.CA].

Massive wave propagation near null infinity.
Preprint, 2023. To appear in Ann. PDE. arXiv:2305.01119 [math.AP].

Hydrogen-like Schrödinger operators at low energies.
Preprint, 2022. To appear in Mem. Amer. Math. Soc. arXiv:2204.08355 [math.AP].

Massive waves gravitationally bound to static bodies.
Proc. Amer. Math. Soc. 152 (2024), 3319-3337. [Link].
arXiv:2312.00959 [gr-qc].

The singularities of Selberg- and Dotsenko--Fateev-like integrals.
Ann. Henri Poincaré 25 (2024), 3957–4032. [Link].
arXiv:2301.03750 [math-ph].

The regularization of Dotsenko--Fateev integrals.
Lett. Math. Phys. 113.100 (2023). [Link].
arXiv:2308.12900 [math-ph]

A strengthened Orlicz--Pettis theorem via Ito--Nisio.
Ann. Funct. Anal. 14.22 (2023). [Link].
arXiv:2210.02495 [math.FA]

Half-waves and spectral Riesz means on the 3-torus, joint with Elliott Fairchild.
Anal. Math. Phys. 12.145 (2022). [Link].
arXiv:2109.10860 [math.NT]

The microlocal irregularity of Gaussian noise.
Studia Math. 266.1 (2022) 1--54. [Link].
arXiv:2012.07084 [math.SP]

There may be slight differences between the versions here and the versions elsewhere. The versions here are the most up-to-date.

Miscellaneous: Link.