I’m a PhD candidate at UC Santa Barbara studying algorithms for quantum physics. I am interested in a good variety of the different ways that quantum physics, information and complexity theory, and pure math intersect. I am advised by Bela Bauer and my research is funded my Microsoft Station Q. My undergrad was at Caltech where I earned a dual B.S. in Math and Physics.
- In 2016, I learned interested in the CSP Dichotomy Conjecture, which was actually proved independently by Zhuk and Bulatov at essentially the same time in 2017. This states that all constraint problems are in P or are NP-Complete. Since quantum constraint problems were known to include at least the additional cases of QMA_1, and MA, I wanted to know what other possibilities there were – the obvious one being BQP, the problems efficiently solvable by a quantum computer. I successfully showed this in 2021, also getting the cases QCMA and coRP in the priocess.
- I was trying to work out some more exact formulas for Quantum State Tomography when I realized that the expressions were in fact matrix permanents. I failed to find an efficient algorithm for computing these formulas, and instead showed that they were NP-hard to compute. But, this resolved an important open problem about the hardness of Positive Semidefinite Permanents, which arise in thermal BosonSampling problems and has been discussed in several contexts.
- My work with my advisor has involved applying Gaussian Fermionic Matrix Product States to more efficiently simulate quasi-1D fermion systems (read: problems involving electrons, where the material is much longer than it is wide). Our paper showed that we could use this to e.g. explore superconductivity at weak couplings much faster and more accurately.
- I have a forthcoming work involving the irrationality measure of pi and the Flint-Hills series, getting a converse of Max Alekseyev’s earlier work.
- The summer before college I worked with the Climate Hazards Center at UCSB’s Geography department. My small portion of the work consisted of trying various ways to filter clouds out of infrared satellite imagery, in order to infer a more complete temperature record. The paper has more citations than the rest of my work combined, ironically.
- In the likely event that this page is out of date (Last Updated: Dec 2021), you can check my Google Scholar.
In high school I co-founded 1064CBread, a competitive computer-hacking team. We won first place in PicoCTF 2013, which was aimed at high schoolers. We then decided to aim higher at the college-level CSAW CTF. To our surprise, we qualified for the finals, and got to fly across the country to NYC. After that we had a decently successful run, becoming finalists or winners in quite a number of competitions and winning prize money here and there. Although we’ve been less active in recent years, we were finalists in Hack-A-Sat 2020, an Air Force competition about satellite hacking, where we won $10k and a satellite.
I’ve also played with UCSB’s team Shellphish a few times, although I’ve never been a core member by any means.
In 2016, I found a security vulnerability in Facebook Messenger and received a bug bounty for reporting it. They promptly fixed it.
In 2012 I found a trivially exploitable vulnerability in a popular online education platform. They have still have not patched it, despite a few reminders on my part.
In 2020 I found a vulnerability in a popular online cloud computing platform. It was patched quicky, but sadly I did not receive a bounty, and they’ve expressed that they would prefer I not talk about it publically – as some users likely using old versions of the software locally and could remain vulnerable.
I’ve enjoyed applying my math knowledge to win some money with Quantiacs. My code has managed several million USD for them over the years, and they came to Caltech and did an inteview with me. It’s given me a useful side-income. I think that a worrying large fraction of quantitative finance is essentially numerology, and that approaches should either rely on news and principals (which I will readily I admit I know nothing about) or principled mathematical foundations - not just drawing lines on a graph or magic numbers.
I’m legally required, I think, to make clear that I’m not providing investment advice! - but if you want to talk math and stocks, I’d be happy to chat. Just email.
I made a simple little game and got it featured on Steam! It’s called Quatris and it’s Free, wow, what a steal! I made it with my friends Charlie and Cole in high school but didn’t put it online until a while later. Hey, it even has achievements!