I am Aidan Backus, a second-year Ph.D. candidate at Brown University; previously I was at UC Berkeley. My main research interest is PDE, 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.

Currently, I am working with Georgios Daskalopoulos on regularity of solutions to Plateau's problem in the hyperbolic plane. Plateau's problem asks for a region of minimal volume which satisfies given boundary data and is motivated by problems involving soap films.

Some other things I'd like to think about: Does the resolvent of the cubic NLS equation, which is a model of Bose-Einstein condensates, have a suitable meromorphic continuation? (I have worked with Profs. Maciej Zworski, who suggested this problem, and Justin Holmer in this area.) Can I use Galois-theoretic methods to optimize my root-multiplicity algorithm with Peter Connick and Joshua Lin for certain infinite-dimensional Lie algebras?

Publications and Preprints

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

  1. The Breit-Wigner series for noncompactly supported potentials on the line (arXiv)
  2. An algorithm for computing root multiplicities in Kac-Moody algebras, with Joshua Lin and Peter Connick (arXiv, implementation in Sage)

Talks given

Summer 2021, Fourier integral operators seminar, UC Berkeley
Properties of Fourier integral operators (Notes)
Summer 2021, Fourier integral operators seminar, UC Berkeley
Oscillatory integrals with linear phase (Notes)
Spring 2021, Complex analysis final exam, Brown University
The uniformization theorem (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
Summer 2020, Scattering theory seminar, UC Berkeley
The scattering matrix in dimension 3
Fall 2018, MUSA Math Mondays, UC Berkeley
Within-host and between-host viral dynamics

Teaching

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.

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

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. I am currently the manager of Clopen Analysis. Come check it out!

Hobbies

Raiding in Final Fantasy XIV is a hobby of mine. I play Paladin for the team "WE ARE NOT OKAY" on Faerie (Aether/NA).

I play viola for the Virtual Video Game Orchestra. Previously I was at the Intermission Orchestra at Cal (where I was also an arranger), the Central Valley Youth Symphony Orchestra, and the San Joaquin County honors high school orchestra.

I also edit the Final Fantasy Wiki and do a lot of technical work for them (bots, FFXIV data mining, writing CSS) for them. If you're interested, check out my site contributions.

Once upon a time, I wrote articles at great length for the Bruin Voice, especially about education policy. You can read some of my work at their website.

I also was once a chair at the Mathematics Undergraduate Student Association of UC Berkeley. I managed a proof-writing seminar and Shadow a Math Major Day.

Nonpublishable writing

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 leecture 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.