I am Aidan Backus, a third-year undergraduate studying mathematics at UC Berkeley. I'm especially interested in PDE and dynamical systems.

I can be reached at aidanbackus@berkeley.edu. You might also read my CV, GitHub, and mathematical blog.

Relevant coursework

Fall 2020
  • 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
  • Spanish 3 — Intermediate Spanish
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)
  • Near Eastern Studies 105A — Ancient Mesopotamian Documents and Literature

Teaching

The following is a list of my teaching posts at UC Berkeley.

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

Time permitting, I also tutor one-on-one, and can provide references upon request. I'm particularly interested in tutoring at the undergraduate level, from calculus to the end-undergraduate classes such as multivariable analysis. If you're interested, contact me and I'll see if we can arrange a time and price.

Writings

Research

In Fall 2019, I am working on my undergraduate thesis, on the Breit-Wigner formula, with Prof. M. Zworski.

In Summer 2019, I developed an efficient algorithm for computing root multiplicities of Kac-Moody 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 within-host 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 between-host age-structure model. See our very early preprint.

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.

  1. Is there a proof of the Peixoto density theorem which avoids the use of the Stone-Weierstrass theorem and Whitney embedding theorem?
  2. Lyapunov exponents and smooth ergodic theory: proof of the Oseledets theorem, etc.
  3. Proof of the Johnson-Geronimo theorem relating uniform hyperbolicity to the resolvent set of the time-one map of a quantum walk.
  4. How fast does the Breit-Wigner approximation converge for a compactly supported ell-infty potential?
  5. 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 and Woodin's program to understand CH.
  6. How well does hyperbolic dynamics extend to the infinite-dimensional case? Is there a good notion of uniform hyperbolicity for evolutionary PDE (whose state space, say, is a Banach manifold)?
  7. The viral age-structure equation: is its Cauchy problem well-posed? Does it have a well-defined notion of basic reproduction number? If so, what are its long-term stability properties?
  8. PDE that are mathematically interesting, but have biological motivation.
  9. Martin-Lof randomness, especially potential applications to ergodic theory.
  10. Relationship between several complex variables and algebraic geometry. Proof of Serre's GAGA theorem.
  11. More generally, are sheaf-theoretic methods at all useful in PDE (say, to extend a local solution to a global solution)?
  12. What is the right definition of magical Kac-Moody algebra? What asymptotic properties do they have?
  13. Sharp bounds on the runtime of the graded ascent algorithm for Kac-Moody algebras we developed. Is the problem of finding multiplicities NP-hard?

Essays on college life

MUSA

As of Spring 2019, I am the Curator of the Mathematics Undergraduate Student Association, responsible for MUSA's funding, website, and proof-writing seminar.

In the 2017-2018 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.

If you're interested in BUMP or MUSA, feel free to contact me at the email given above.

Web design

As mentioned above, I designed the MUSA website, and have also contributed to the Final Fantasy Wiki, and, in a previous life, the Bruin Voice.

If you'd like to commision a personal website, please contact me, and I'll see if I can't find time and negotiate a price.

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.

Now, most of my writing is mathematical; what's not is mostly fiction tied to Dungeons and Dragons, where I have GM'd two campaigns: a political fantasy called The Cycle of Helix, and its distant sequel, an urban fantasy called Spice and Warforged. If I'm ever satisfied with any of my fiction, I'll possibly post it here.

Miscellany

I have solutions to a handful of Project Euler problems, written in C, viewable.

I write LaTeX (and anything else, for that matter) using vim. You can download my .vimrc.