Jalex Stark |

I currently work as a research assistant in the CMS department at Caltech. In Fall 2018, I'll begin as a PhD student in the UC Berkeley CS theory group.

Here is my CV, last updated for graduate school applications.

Here is my blog.

Email: jalex at caltech dot edu

Research Questions |

**My favorite "big" open questions include:**

- The quantum PCP conjecture.
- Are there efficient constructions for O(log n)-Ramsey graphs?
- 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? (and by way of implication, does P = PSPACE?)
- Does C_q = C_qs? That is, are there bipartite correlations which can be obtained by spacelike-separated parties using infinite-dimensional tensor-product entanglement, but not by parties using finite-dimensional entanglement?

**Some of my favorite "less big" open questions include:**

- For which dimensions d can we self-test the maximally entangled state of dimension d with a two-prover game? (Matthew Coudron and Anand Natarajan show how to do this for d = 2
^{2n}. Coladangelo, Koh, and Scarani show how to self-test arbitrary states using correlations which are not games.) - Is there an algorithm to decide C_qa, even with access to an oracle for the halting problem? (William Slostra shows that is undecidable; this question asks for a matching upper bound.)
- Which NP-complete problems have QMA-complete analogues?

Papers |

- Separation of finite and infinite-dimensional quantum correlations, with infinite question or answer sets (Abstract)

Preprint, 2017.

Works in Progress |

- An expository note about a countable hat game and the importance of measurability.
- Very rough notes on the computational complexity of noncommutative graphs.

Mathematical Notes |

- An edX course on quantum cryptography taught by Professors Thomas Vidick and Stephanie Wehner. (I contributed homework and quizzes for weeks 4 and 7.)
- A 3-day course on ordinal arithmetic that I taught at Canada/USA Mathcamp 2015
- 2 days of a 4-day course on P vs. NP co-taught with Adam Hesterberg at Canada/USA Mathcamp 2015.
- Scribed notes for Ma 191: Geometrical Paradoxes, taught by Professor Alexander Kechris in Winter 2015.

Talk Slides |

- Wizards vs. Time Travel, Jan 6, 2017, Caltech Undergraduate Math Club.

Abstract:(Click to show)

Travel |

**Upcoming**

- (Apr 19 -- Apr 25) I'll be at UT Austin visiting collaborator William Hoza.
- (June 28 -- Aug 10) I'll be a Junior Counselor at Canada/USA Mathcamp 2017.

**Past**

(Show/hide)

Service |

- I previously organized the Caltech undergraduate math seminar, now organized by Tynan Ochse and Felix Weilacher.
- In 2015 and 2016, I organized the Caltech Harvey Mudd Math Competition, a one-day, on-site math competition for high school students.

Diversions |

- 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.