Adviser: Ryan Williams
Previously I was a PhD student at Stanford and an undergraduate at Oxford.
For more, see my CV below.
|Teaching in Fall 2021: 6.042: Math for Computer Science|
2020 Fall: 6.006 (TA)
2020 Spring: 6.045 (TA)
2019 Fall: 6.006 (TA)
2019 Spring: 6.045 (TA)
2018 Fall: 6.854 (TA)
Research InterestsCollectively, our knowledge of algorithms far exceeds our knowledge of lower bounds. For millennia, we have advanced as a society largely by developing more efficient tools, processes, and algorithms, but proving limits on the power of computation wasn't really even a meaningful aim before the seminal work of Church and Turing provided a precise mathematical definition of computation. Decades later, we still know relatively little about its limits. Many problems are currently hard for computers to solve (and are believed to be provably hard), such as the problem of falsifying bank transactions. But will some brilliant algorithmist be able to solve such problems tomorrow? Somewhat embarrassingly, we don't actually know! Formal proofs of hardness continue to elude us, and in fact there is much pessimism in the field of complexity theory because of proof "barriers" showing that certain classes of proofs will never be able to resolve some of the central open problems in complexity theory, like P vs NP. My research focuses on circumventing proof barriers and exploiting dualities between upper and lower bounds. Using algorithmic techniques, we can develop new frameworks for proving lower bounds, and conversely, strong lower bounds can yield efficient algorithms for related problems!
About MeI grew up mostly in Tallahassee, Florida and near Portland, Oregon. In my free time, I can usually be found drinking tea, napping, or getting totally wrecked at some kind of game by children, smaller children, and even blindfolded opponents.