I am Aidan Backus, a fourthyear undergraduate studying mathematics at UC Berkeley. I'm especially interested in PDE, harmonic analysis, and dynamical systems. I also like logic and mathematical biology!
I can be reached at aidanbackus@berkeley.edu. You might also read my CV, GitHub, and mathematical blog.
Relevant coursework
 Spring 2020
 Math 219 — Dynamical Systems
 Math 225B — Metamathematics: Recursion Theory
 Fall 2019

 Math 208 — C*Algebras
 Math 212 — Several Complex Variables
 Math 278 — Topics in Analysis: General Relativity in Spherical Symmetry
 Spring 2019

 Math 202B — Introduction to Topology and Analysis
 Math 250B — Commutative Algebra
 Math 222B — Partial Differential Equations
 Fall 2018

 Math 202A — Introduction to Topology and Analysis
 Math 250A — Groups, Rings, and Fields
 Math 125A — Mathematical Logic
 Philosophy 149 — Special Topics in the Philosophy of Logic and Mathematics (Nonclassical Logic)
 Spring 2018

 Math H185 — Honors Introduction to Complex Analysis
 Math 105 — Second Course in Analysis
 Math 114 — Galois Theory
 Physics 137A — Quantum Mechanics
 Fall 2017

 Math H104 — Honors Introduction to Analysis
 Math 113 — Introduction to Abstract Algebra
 Math 126 — Introduction to Partial Differential Equations
 CS 170 — Efficient Algorithms and Intractable Problems
 Spring 2017

 Math 110 — Linear Algebra
 Math 55 — Discrete Math
 CS 61B — Data Structures
 Fall 2016
 Math 54 — Linear Algebra and Differential Equations
 CS 61A — Structure and Interpretation of Computer Programs
 Physics 7A — Physics for Scientists and Engineers (Classical Mechanics)
Teaching
The following is a list of my teaching posts at UC Berkeley.
 Fall 2019
 Student Instructor, Math 185 — Complex Analysis
Organizer, MUSA 74 — ProofWriting Skills
 Spring 2019
 Reader, Math 105 — Second Course in Analysis
Organizer, MUSA 74 — ProofWriting 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
Time permitting, I also tutor oneonone, and can provide references upon request. I'm particularly interested in tutoring at the undergraduate level, from calculus to the endundergraduate classes such as multivariable analysis. If you're interested, contact me and I'll see if we can arrange a time and price.
Writing
 My notes. A hodgepodge of notes from various classes I've taken that I refer back to occasionally. Currently includes notes on complex analysis (Riemann mapping theorem, domains of holomoprhy, etc.), algebraic geometry (Kodiara embedding theorem, Bergman kernel asymptotics), general relativity (cosmic censorship, the Cauchy problem), and C*algebras (noncommutative dynamical systems, noncommutative geometry, the GelfandNaimark theorem). Any errors and sketchiness were surely my own doing, please don't hound my professors over it!
 The BreitWigner formula. My senior thesis (Spring 2020), coming soon.
 An algorithm for computing root multiplicities in KacMoody algebras, now on the arXiv! Original research (with Joshua Lin et al.) giving a new algorithm for computation of root multiplicities of KacMoody algebras. You can also view an implementation in Sage, to be optimized and submitted to the Sage Project soon!
 Formalizations of analysis. A more philosophical paper discussing Bishop's constructive analysis, Brouwer's intutionistic program, and pointless topology. Written for Philosophy 149 (Fall 2018).
 Mathematical models linking withinhost and betweenhost HIV dynamics with Dr. Naveen Vaidya et al. A summary of work done in viral dynamics at the San Diego State REU (Summer 2018), to be cleaned up and turned into two papers to be submitted soon!
 Baire classes and the Borel sigmaalgebra. An extracredit assignment for Math H104 (Fall 2017) which gives an exposition of the existence of a Baire function for every countable ordinal on every Polish space. Written before I knew how to use TikZ or knew any logic, so very amateurish. Maybe I'll clean it up some day.
 Cuneiform arithmetic (PPT), a historical presentation for Near Eastern Studies 105A (Fall 2016), as well as presenter notes.
 On how to get into an REU, based on my experiences.
Research
In 20192020, I am working on my undergraduate thesis, on the BreitWigner formula, with Prof. M. Zworski.
In Summer 2019, I developed an efficient algorithm for computing root multiplicities of KacMoody algebras under Prof. Richard Borcherds, and proved some asymptotic results about the growth rates of multiplicities.
In Summer 2018, I was at the Disease Modeling Lab in San Diego State University, under the direction of Dr. Naveen Vaidya. We gave a withinhost model for computing the probability of transmission of HIV as a function of age of infection. We then used the computed probabilities as parameters in a betweenhost agestructure model.
Other math
I was at the Houston Summer School in Dynamics in Fall 2019!
Here's some questions I'd like to know the answer to, or at least concepts I'd like to understand, in no particular order. Most of them are not open problems (but some are), but if you can explain any of them to me, I owe you a bottle of peach soju. I have also taken the liberty of using a lot of words I don't fully understand  I'm just a student, after all.
 Is there a proof of the Peixoto density theorem which avoids the use of the StoneWeierstrass theorem and Whitney embedding theorem?
 How fast does the BreitWigner approximation converge for a compactly supported ellinfty potential? Does it remain formally valid for a superexponentially decaying potential?
 Large cardinals: the relationship between properties of ultrafilters, their respective large cardinals, elementary embeddings and class models; supercompactness and extender models; the Ultimate L axiom.
 How well does hyperbolic dynamics extend to the infinitedimensional case? Is there a good notion of uniform hyperbolicity for evolutionary PDE (whose state space, say, is a Banach manifold)?
 The viral agestructure equation: is its Cauchy problem wellposed? Does it have a welldefined notion of basic reproduction number? If so, what are its longterm stability properties?
 PDE that are mathematically interesting, but have biological motivation.
 MartinLof randomness, especially potential applications to ergodic theory.
 Algebraic geometry over the complex plane, especially GAGAtype results.
 Are sheaftheoretic methods at all useful in PDE (say, to extend a local solution to a global solution)?
 What is the right definition of magical KacMoody algebra? What asymptotic properties do they have?
 Is the problem of computing root multiplicities of KacMoody algebras NPhard?
MUSA
Until 2019, I was the Curator of the Mathematics Undergraduate Student Association, responsible for MUSA's funding, website, and proofwriting seminar. I am still responsible for the proofwriting seminar.
In the 20172018 school year, I was an Outreach Chair along with Ning McKenzie and Joshua Lin, and responsible for organizing Shadow a Math Major Day, with Yu Ma.
Hobbies
Raiding in Final Fantasy XIV is a hobby of mine, though I'm not very good at it.
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 the wiki Github and 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.