I was a graduate student at Princeton working with Nick Katz until May 2016, and starting in September I am a junior fellow at ETH-ITS. I study arithmetic algebraic geometry - primarily applications of algebraic geometry to analytic number theory. I have collaborated on work in compressed sensing, category theory, expander graph theory, and extremal combinatorics, and I hope to work on many more different topics in the future.
PDF of On cap sets and the group-theoretic approach to matrix multiplication (2016), with Jonah Blasiak, Thomas Church, Henry Cohn, Joshua A. Grochow, Eric Naslund, and Chris Umans.
Arxiv link of On cap sets and the group-theoretic approach to matrix multiplication (2016), with Jonah Blasiak, Thomas Church, Henry Cohn, Joshua A. Grochow, Eric Naslund, and Chris Umans.
On cap sets and the group-theoretic approach to matrix multiplication (2016), with Jonah Blasiak, Thomas Church, Henry Cohn, Joshua A. Grochow, Eric Naslund, and Chris Umans.
PDF of On numerical Newton-Okounkov bodies and the existence of Minkowski bases (2016), with David Schmitz.
Arxiv link of On numerical Newton-Okounkov bodies and the existence of Minkowski bases (2016), with David Schmitz.
On numerical Newton-Okounkov bodies and the existence of Minkowski bases (2016), with David Schmitz.
PDF of The growth rate of tri-colored sum-free sets (2016), with Robert Kleinberg and David E. Speyer.
Arxiv link of The growth rate of tri-colored sum-free sets (2016), with Robert Kleinberg and David E. Speyer.
The growth rate of tri-colored sum-free sets (2016), with Robert Kleinberg and David E. Speyer.
PDF of Upper bounds for sunflower-free sets (2016), with Eric Naslund.
Arxiv link of Upper bounds for sunflower-free sets (2016), with Eric Naslund.
Upper bounds for sunflower-free sets (2016), with Eric Naslund.
PDF of Bilinear Forms with Kloosterman Sums and Applications (2016), with Emmanuel Kowalski and Philippe Michel.
Arxiv link of Bilinear Forms with Kloosterman sums and applications (2016), with Emmanuel Kowalski and Philippe Michel.
Bilinear forms with Kloosterman sums and applications (2016), with Emmanuel Kowalski and Philippe Michel.
PDF of Rational Cohomology Tori (2015), by Olivier Debarre, Zhi Jiang, and Martí Lahoz, with an appendix by William F. Sawin.
Arxiv link of Rational Cohomology Tori (2015), by Olivier Debarre, Zhi Jiang, and Martí Lahoz, with an appendix by William F. Sawin.
Non-existence of smooth rational cohomology tori of general type - appendix to Rational Cohomology Tori (2015) by Olivier Debarre, Zhi Jiang, and Martí Lahoz.
PDF of Positivity of GIT heights of zero-cycles and hyperplane arrangements (2015), with Ashwath Rabindranath.
Arxiv link of Positivity of GIT heights of zero-cycles and hyperplane arrangements (2015), with Ashwath Rabindranath.
Positivity of GIT heights of zero-cycles and hyperplane arrangements (2015) with Ashwath Rabindranath.
PDF of Ordinary Primes for Abelian Surfaces (2015).
Arxiv link of Ordinary Primes for Abelian Surfaces (2015).
Ordinary primes for abelian aurfaces (2015).
PDF of Ramanujan Coverings of Graphs (2015), with Chris Hall and Doron Puder.
Arxiv link of Ramanujan Coverings of Graphs (2015), with Chris Hall and Doron Puder.
Ramanujan coverings of graphs (2015) with Chris Hall and Doron Puder.
PDF of Kloosterman paths and the shape of exponential sums (2014), with Emmanuel Kowalski.
Arxiv link of Kloosterman paths and the shape of exponential sums (2014), with Emmanuel Kowalski.
Kloosterman paths and the shape of exponential sums (2014) with Emmanuel Kowalski.
PDF of Notes on commutation of limits and colimits (2014), with Marie Bjerrum, Peter Johnstone, and Tom Leinster.
Arxiv link of Notes on commutation of limits and colimits (2014), with Marie Bjerrum, Peter Johnstone, and Tom Leinster.
Notes on commutation of limits and colimits (2014) with Marie Bjerrum, Peter Johnstone, and Tom Leinster.
PDF of Certifying the restricted isometry property is hard (2012), with Afonso S Bandeira, Edgar Dobriban, and Dustin G Mixon.
Arxiv link of Certifying the restricted isometry property is hard (2012), with Afonso S Bandeira, Edgar Dobriban, and Dustin G Mixon.
Certifying the restricted isometry property is hard (2012) with Afonso S. Bandeira, Edgar Dobriban, and Dustin G. Mixon.
PDF of An Elementary Proof that Vector Bundles on P1 Split (2011)
Arxiv link of An Elementary Proof that Vector Bundles on P1 Split (2011)
An elementary proof that vector bundles on P1 split (2011).