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
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 = 22n. 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?
- 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.