I graduated in 2018 from Princeton University.My advisers were Christopher Skinner and Shouwu Zhang. I have now moved to MIT. Previously, I was also an undergraduate at Princeton and graduated in 2014.
In the Fall of 2016, I visited the I.H.E.S..
I am interested in algebraic number theory, particularly in arithmetic geometry and Iwasawa theory. Most recently I have constructed supersingular Rankin-Selberg p-adic L-functions for imaginary quadratic fields in the style of Katz, Bertolini-Darmon Prasanna and Liu-Zhang-Zhang, resolving questions about the existence of such p-adic L-functions dating back to the 70s. I have also established special value formulas for these p-adic L-functions and explored their arithmetic applications. Previously, I did work with Chao Li on establishing the rank and p-parts of the Birch and Swinnerton-Dyer conjecture for quadratic twist families of elliptic curves over Q, in particular showing that a positive proportion of quadratic twists satisfy rank BSD whenever the curve has a rational 3-isogeny (thus verifying a weak version of Goldfeld's conjecture for such curves). We also establish similar results for the Mordell sextic twists family y^2 = x^3 + k, showing a positive proportion have rank 0 (resp. 1). I have also done work in geometric topology regarding the Heegaard-Floer and Khovanov homologies of knot theory.
Here are some of my recent papers.
A New p-adic Maass-Shimura operator and supersingular Rankin-Selberg p-adic L-functions.
Prime twists of elliptic curves (with Chao Li), to appear in Mathematical Research Letters.
Goldfeld's conjecture and congruences between Heegner points (with Chao Li), accepted to Forum of Mathematics, Sigma.
A Galois cohomological proof of Gross's factorization theorem, submitted.
Generalized Heegner cycles at Eisenstein primes and the Katz p-adic L-function, Algebra and Number Theory vol. 10, no 2, 2016, pp. 309-374. Arxiv (minor differences from the published version)
On a conjecture concerning the maximal cross number of unique factorization indexed sequences, appeared in J. Number Theory, vol 133, 9 (September 2013), 3033-3056. This paper is a result of the research I did as a participant in the Duluth REU, run by Professor Joe Gallian at the University of Minnesota Duluth.
A spanning tree cohomology theory for links (with Igor Kriz), appeared in Advances in Mathematics, vol 255, 1 (April 2014), 414-454. Arxiv
Field theories, stable homotopy theory, and Khovanov homology (with Po Hu, Igor Kriz), Topology Proceedings, vol 48, 2016, pp. 327-360. Arxiv
Here is an introductory article to Étale cohomology, written for the final project of my algebraic geometry class with Nick Katz in Spring 2012.
An Excursion into Étale Cohomology.