I am Aidan Backus, a third-year Ph.D. candidate at Brown University; previously I was at UC Berkeley. My main research interest is PDE, especially its geometric and numerical-analytic aspects, but I generally enjoy interdisciplinary parts of mathematics.

I can be reached at aidan_backus@brown.edu. You might also read my CV, GitHub, and blog Some Compact Thoughts, or check out the community-written real analysis textbook, Clopen Analysis.

Recently I've been thinking about least-gradient and best-Lipschitz functions, advised by George Daskalopoulos; see my recent research statement for more on that. I've also recently been interested in the fractal uncertainty principle and the scattering theory of resonances.

You can click on the titles of these papers to read their abstracts.

*The fractal uncertainty principle via Dolgopyat's method in higher dimensions*(joint with James Leng and Zhongkai Tao, in preparation)*Functions of least gradient in constant curvature*(in preparation)*The Breit-Wigner series for noncompactly supported potentials on the line*(2020, arXiv version)*An algorithm for computing root multiplicities in Kac-Moody algebras*(joint with Peter Connick and Joshua Lin, 2019, arXiv, implementation in Sage)

- Fall 2021, Grad Student Seminar, Brown University
- Nonlinear Laplace equations
- Summer 2021, Fourier integral operators seminar, UC Berkeley
- Properties of Fourier integral operators (Notes); Oscillatory integrals with linear phase (Notes)
- Spring 2021, Grad Student Seminar, Brown University
- An ultrapowerful proof technique, the Nullstellensatz, and Sendov's conjecture
- Fall 2020, MUSA Math Mondays, UC Berkeley
- Numbers Big and Small: Calculus, ultrapowers, and measurability
- Summer 2020, Scattering theory seminar, UC Berkeley
- Resonance-free regions I: The geometry of trapping, nontrapping estimates, and semiclassical defect measures; The scattering matrix in dimension 3

The following is a list of my teaching posts. Prior to Fall 2021, all such teaching posts have been at UC Berkeley; after, all posts are at Brown University unless otherwise noted.

- Spring 2022
- Teaching Assistant, Math 100 — Calculus II
- Fall 2021
- Teaching Assistant, Math 90 — Calculus

Reader, Math 523 (Wesleyan University) — Topology - Summer 2021
- Reader, Math 110 — Linear Algebra
- Spring 2021
- Reader, Math 140 — Metric Differential Geometry
- Fall 2020
- Reader, Math 202A — Topology and Analysis
- Summer 2020
- Reader, Math 110 — Linear Algebra
- Spring 2020
- Reader, Math 202B — Topology and Analysis

Organizer, MUSA 74 — Proof-Writing Skills - Fall 2019
- Student Instructor, Math 185 — Complex Analysis

Organizer, MUSA 74 — Proof-Writing Skills - Summer 2019
- Reader, Math 1A — Calculus
- Spring 2019
- Reader, Math 105 — Second Course in Analysis

Organizer, MUSA 74 — Proof-Writing Skills - Fall 2018
- Reader, Math H104 — Honors Introduction to Mathematical Analysis
- Spring 2018
- Reader, Math 104 — Introduction to Mathematical Analysis
- Fall 2017
- Academic Intern, CS 61A — Structure and Interpretation of Computer Programs

Clopen Analysis is a community-written graduate-level real analysis textbook that strives to operate at a high level of abstraction while still providing lots of concrete examples and applications. Come check it out!

- Aidan Backus.
**The Breit-Wigner series and distribution of resonances of potentials** - My undergraduate thesis.
- Aidan Backus.
**Formalizations of analysis** - My final project for nonclassical logic at UC Berkeley.
- Naveen Vaidya, Angelica Bloomquist, et al.
**Mathematical Models for Linking Within-Host and Between-Host Viral Dynamics: The Effect of Antibodies on the Probability of Transmission** - A report on work done at the 2018 San Diego State University REU.
- Aidan Backus.
**My undergraduate analysis lecture notes** - Banach-valued measure theory. Ergodic theory and the Hopf argument. The Toda lattice and its applications to the QR algorithm. Siegel's KAM theorem. The holomorphic functional calculus. C*-representation theory of locally compact groups. Noncommutative geometry. Hormander's \dbar estimates. Bergman kernels and their application to Chow's theorem. Pseudodifferential calculus and the FBI transform. The Cauchy problem in general relativity. Cosmic censorship in spherical symmetry.
- Aidan Backus.
**My undergraduate logic lecture notes** - The Goedel completeness and incompleteness theorems. Kleene's recursion theorem. Induction in weak subtheories of PA. Forcing and Cohen's theorem. Turing degrees and the axiom of determinacy. Consistency of GCH. Large cardinals under a measurable cardinal. Measurable cardinals and their inner models. The Kunen calamity. Supercompact cardinals and their inner models. The Ultimate L.