Welcome to my homepage!

I’m a DPhil student in computer science at Oxford University, where I work on algorithmic verification with James Worrell and Joel Ouaknine (as of 2023). I grew up in Goa, India, and studied math at IISc Bangalore. If something on this site interests you, I’d love to chat – I’m julianrdcosta on gmail and twitter.

### Work With Me

Although I dabble in many things, I’m particularly interested in working in:

- Software Verification: I have little practical experience in building verified software so far, but I know some of the theory thanks to my PhD
- Crypto: I’m just dipping my toes into the space right now, but I’m familiar with cryptography and theoretical computer science
- Quantum Computing: Ask me about this after October 2022, until then you might enjoy Qubits and the Kernel Trick: The power of working in a bigger space
- Drug Design: My team (led by Preetham Venkatesh) won the Indian government’s Drug Discovery Hackathon 2020. You may like Generating SARS-CoV-2 Protease Inhibitors with Variational Autoencoders and Notes on AlphaFold2
- AI Alignment: You may like Pascal’s Mugging: Reasoning when you have other things to do
- Math Education: I help run Monsoon Math, a camp for high school students, and care a lot about high quality pedogogy. You may like The Shortest Proof of Godel’s Incompleteness Theorems and Markov Chains, Mixing Times and Couplings

I also have a LinkedIn and a CV.

If you are an unusually enlightened parent, child, or human, you may enjoy hiring me as an aristocratic tutor.

### Research Papers

I’m currently thinking about discrete linear dynamical systems with perturbations. For example, see this blog post about the 2D Rotation Rounding Problem.

The Pseudo-Reachability Problem for Diagonalisable Linear Dynamical Systems

Bounding the Escape Time of a Linear Dynamical System over a Compact Semialgebraic Set.

On the Complexity of the Escape Problem for Linear Dynamical Systems over Compact Semialgebraic Sets

The Pseudo-Skolem Problem is Decidable

How Fast Can You Escape a Compact Polytope? (STACS 2020)

Erratum: Appendix 2: Proof of Lemma 5 of How Fast.. deals with converting a rational matrix A to its Jordan form J = QAQ^{-1} where Q^{-1} is the matrix of generalized eigenvectors. It contains the sentence “The entries q ij of Q can be computed in 3d^3 operations from the entries of Q^{−1}”. Unfortunately this is not valid, because the entries of Q^{-1} are algebraic numbers, which may not be representable explicitly, so it is not clear what it would mean to use Gaussian elimination (which has cubic complexity) on them. It is, however, true that the entries of Q, J and Q^{-1} can be computed in polynomial time from A, but this involves careful maneuvering to avoid going through the splitting field of all the eigenvalues of A, and Q is not computed from Q^{-1}. The details are in Jin-Yi Cai’s 1996 paper Computing Jordan Normal Forms Exactly for Commuting Matrices in Polynomial Time. This means that the explicit constants in Theorem 3 are incorrect. I am hoping to publish a followup which improves Theorem 3 to a single exponential bound.

### Interests

Right now I’m interested in AI, especially questions in theory and alignment, neuroscience, synthetic and molecular biology, longevity research, economics – how is wealth created?, education and parenting, and design.

#### Idiolect

Words and phrases that have made it into my personal vocabulary and I’d like to see get more popular

Today’s lucky ten thousand – a short handle for the idea that someone not knowing something isn’t an occasion for surprise or scorn, but an opportunity to watch someone discover something for the first time

Finite problems – The human mind tends to expand or contract all problems to roughly the size that will occupy an entire brain. As a relatively privileged person, I use the phrase finite problems to remind myself that most of the problems I face are not likely to leave me homeless or starving, but can – worst case scenario – be dodged by disappearing, changing my name, and returning as Julian Prime. This thought comforts me. It is unlikely to work for someone else, but I write it up because it might.

Nerdsnipe – It’s just really fun to use as a verb

#### Questions

Stuff I’d really like to know the answer to:

- What are the base rates for Chronic Fatigue Syndrome, developing CFS-like symptoms after respiratory infection, and developing CFS-like symptoms after Covid?
- Given the insane corruption and decadence of 16-century Popes, how did the Papacy survive for another 5 centuries with its reputation sufficiently intact to be considered a moral authority? Essentially, I want know, what are the reasons behind the Roman Catholic Church’s longevity?
- What parts of the modern world /economy actually produce wealth (in the Paul Graham sense, also excluding positional goods) , which parts are bullshit (in the bullshit jobs sense) and are there any things which are neither?

#### Requests/Gifts

(if for some reason you feel inclined)

I would like to read the following books, which are pretty hard to get hold of:

~~The Marlow books by Antonia Forest~~(managed to procure print copy of Autumn Term)~~All the Fishes Come Home to Roost, by Rachel Manija Brown~~(managed to find ebook)~~Pogo by Walt Kelly (collections of the comic strips)~~(found in New York)- Asimov Laughs Again