I consider myself a theorist in the broad sense: I like to consider compelling-but-vaguely-specified problems, find formal statements that carry some of their essence, and then attack the formal questions with the tools of mathematics, computer science, physics, philosophy, etc. In my current work on algorithmic trading, I'm learning to add computers and data to this picture. This is slow-going.

I was formerly currently a quantitative researcher at Jane Street Group. I consider myself an effective altruist. Before that, I was a graduate student in the CS theory group at UC Berkeley, advised by Umesh Vazirani. Before that, I was an undergrad at Caltech, advised by Thomas Vidick. Here is a CV, updated August 2019. Here is my archived undergrad blog. Email: jalex at cs dot berkeley dot edu

My first name rhymes with the more common "Alex". In particular, my name is not pronounced like "Jay-lex". My given name is "Jacob Alexander Stark", and this is reflected in some of my official records. Etymologically, my first name is a contraction of my given first and middle names.

I don't like playing masculine roles or being identified as a man. If you refer to me with pronouns "they" and "them," I'll be more comfortable around you than if you refer to me with pronouns "he" and "him". I won't remind you of this unless we have a conversation about it. 

I accept anonymous feedback here. I especially appreciate being told that some specific actions I've taken are likely to hurt people. I'm worse than average at noticing and interpreting social cues.

I spend most of my days working on specific (proprietary) instances of the general problem "design and enact decision procedures that identify market inefficiencies as well as possible, measured in terms of maximizing the ratio (expected value in dollars of trading against the inefficiency) / (amount of human time required to find the inefficiency and execute the trades).

Accordingly, I'm very interested in questions about 

• human psychology, especially in the sense of biases that cause large deviations from expected utility maximization
• deriving the behavior of systems of many agents from facts about the individual agents, a la macroeconomics and statistical mechanics
• statistical learning theory, especially to the extent that one can design empirically effective ad hoc inference algorithms by using analogies to provably correct ones

Outside of algorithmic trading, I'm interested in finding structural changes to collaboration that accelerate the pace of scientific research. Some of my favorite things in this space include

• reinventing discovery, a book by michael nielsen about science in the age of networks
• bridging the gap between intuitive knowledge and formal knowledge, especially via writing machine checkable proofs
• stackexchange + mathoverflow, sites designed for technical professionals to ask and answer very specific questions
• the emergent ventures project by the mercatus center, and in general any attempts to use startup-like models for academic-like projects
• LessWrong and alignmentforum, group blogs dedicated respectively to general rationality and AI alignment
• Ought, a small nonprofit research lab, and specifically their factored cognition and dialog markets projects.

I used to participate in academic computer science. The following legacy bullets were written in that time. 

Here are questions which I think are morally relevant and where theorists may be able to make significant contributions:

• How should one act in the presence of uncertainty about the merits of various moral systems? See e.g. William MacAskill's PhD thesis. 
• Is it possible in principle, disregarding engineering constraints, to design an agent X such that (after an appropriate training period), X can accomplish your goals better than you can? See e.g. Paul Christiano's proposal for a meta-algorithm (IDA) for this problem. As a concrete question: can we find a toy model in which some instantiation of IDA provably works? Conversely, can we find a toy model in which there is a provable barrier to IDA-type algorithms?

My favorite "big" open questions inside of academic computer science include:

• The quantum PCP conjectures.
• Does QMA = QCMA? That is, for all problems with quantum proofs which can be efficiently verified by a quantum computer, does the same problem have classical proofs which can be easily verified by a quantum computer? (Resolving this question in an unconditional sense would separate P and PSPACE. I'm interested in evidence towards this question, say by stronger kinds of oracle separations than are currently known.)

You can also see these on my google scholar profile.

• Trading locality for time: certifiable randomness from low-depth circuits (Abstract)
  The generation of certifiable randomness is the most fundamental information-theoretic task that meaningfully separates quantum devices from their classical counterparts. We propose a protocol for exponential certified randomness expansion using a single quantum device. The protocol calls for the device to implement a simple quantum circuit of constant depth on a 2D lattice of qubits. The output of the circuit can be verified classically in linear time, and contains a polynomial number of certified random bits under the sole physical assumption that the device used to generate the output operated using a (classical or quantum) circuit of sub-logarithmic depth. This assumption contrasts with the locality assumption used for randomness certification based on Bell inequality violation and more recent proposals for randomness certification based on computational assumptions. Our procedure is inspired by recent work of Bravyi et al. (arXiv:1704.00690), who designed a relation problem that can be solved by a constant-depth quantum circuit, but provably cannot be solved by any classical circuit of sub-logarithmic depth. We expand the discovery of Bravyi et al. into a framework for robust randomness expansion. Furthermore, to demonstrate randomness generation it is sufficient for a device to sample from the ideal output distribution within constant statistical distance. Our proposal can thus be interpreted as a proposal for demonstrated quantum advantage that is more noise-tolerant than most other existing proposals that can only tolerate multiplicative error, or require additional conjectures from complexity theory. Our separation does not require any conjectures, but assumes that the adversarial device implements a circuit of sub-logarithmic depth.
  with Matthew Coudron and Thomas Vidick. Technical report, arxiv:1810.04233
  QIP 2019.
• Unconditional separation of finite and infinite-dimensional quantum correlations (Abstract)
  Determining the relationship between quantum correlation sets is a long-standing open problem. The most well-studied part of the hierarchy is captured by the chain of inclusions C_q⊆C_qs⊆C_qa⊆C_qc. The separation C_qs≠C_qa, showing that the set of quantum spatial correlations is not closed, was proven in breakthrough work by Slofstra [arXiv:1606.03140 (2016), arXiv:1703.08618 (2017)]. Resolving the question of C_qa=C_qc would resolve the Connes Embedding Conjecture and would represent major progress in the mathematical field of operator algebras. In this work, we resolve the ambiguity in the first inclusion, showing that C_q≠C_qs. We provide an explicit construction of a correlation that can be attained on a tensor product of infinite-dimensional Hilbert spaces but not finite-dimensional ones. This property is also conjectured to be possessed by any correlation which maximally violates the I₃₃₂₂ inequality.
  with Andrea Coladangelo. Technical report, arxiv:1804.05116.
  QIP 2019, best student paper prize.
• Robust self-testing for linear constraint system games (Abstract)
  We study variants of the Mermin--Peres Magic Square and Magic Pentagram with outputs over alphabets of size d. We show that these games have unique winning strategies requiring 2 and 3 pairs of maximally entangled qudits, respectively. We also show that this uniqueness is robust to small perturbations, and we show the same for a certain n-fold product of these games. These games are the first nonlocal games which robustly self-test maximally entangled qudits for dimensions other than powers of 2. In order to prove our result, we extend the representation-theoretic framework of Cleve, Liu, and Slofstra (Journal of Mathematical Physics 58.1 (2017): 012202.) to apply to linear constraint games over ℤ_d for d≥2. We package our main argument into a general self-testing theorem which can be applied to various linear constraint games.
  with Andrea Coladangelo. Technical report, arxiv:1709.09267.
  Presented at QIP 2018. (Video) (Slides)
• Separation of finite and infinite-dimensional quantum correlations, with infinite question or answer sets (Abstract)
  Tsirelson's problem concerns the relationships between the sets of correlations which arise from different models of quantum mechanics. To summarize briefly, we have C_q⊆C_qs⊆C_qa⊆C_qc, where C_q are the correlations achievable by finite-dimensional quantum systems, C_qs the correlations achievable in the spatial tensor product model, C_qa the correlations which are arbitrarily well-approximated by correlations in C_q, and C_qc the correlations achievable in the commuting operator model. The question of separating C_qa from C_qc is equivalent to Connes' Embedding problem. The separation C_qs ≠ C_qa was resolved by Slofstra in 2017. Our work focuses on the existence of a separation of C_q from C_qs.
  We show that if we allow to measure correlations between countably many variables (questions) or if we allow to measure correlations between variables with countably many possible outcomes (answers), then there are correlations which can be achieved with infinite-dimensional spatial tensor product systems but not finite ones. In other words, we give a separation of the new correlation classes C_q^∞ ≠ C_qs^∞ which are infinite. This seems to provide evidence in support of the "real world" separation C_q ≠ C_qs, which remains unproven.
  with Andrea Coladangelo. Technical report, arxiv:1708.06522.

• A 3-day course on ordinal arithmetic, taught at Canada/USA Mathcamp 2015.
• Slides for Wizards vs. Time Travel, Jan 6, 2017, Caltech Undergraduate Math Club.
  Abstract:
   (Click to show)

For thinking in general

• Thinking, Fast and Slow by Kahneman
• Rationality: AI to Zombies by Yudkowsky
• Algorithms to Live By by Christian and Griffiths

For doing theory

• An edX course on quantum cryptography taught by Professors Thomas Vidick and Stephanie Wehner.
• Lecture notes on quantum computation by John Preskill
• Scirate, the easiest way to catch important posts to arxiv/quant-ph
• Canada/USA Mathcamp, a summer program where grad students teach cool theorems to bright high school students. If you're in either group, do apply!
• Quantum Computing Stack Exchange. A community still in its infancy --- a good place to ask questions about the field, both general and specific.

• Ditch Day for Cranks, a fake Ditch Day stack (read: themed run-around and puzzle activities) based in part on parodying Professor Nets Katz' wonderful course Ma1a and associated text Calculus for Cranks.