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(Pre)publications

For reprints (or rather electronic reprints), just shoot me an email.
  1. Shapes of sextic fields and log-terms in Malle's conjecture (with Erik Holmes)
    In preparation
  2. The shapes of Galois quartic fields (with Piper H)
    To appear in Transactions of the American Mathematical Society
  3. Equidistribution of shapes of complex cubic fields of fixed quadratic resolvent
    To appear in Algebra and Number Theory
  4. Explicit computations of Hida families via overconvergent modular symbols (with Evan Dummit, Marton Hablicsek, Lalit Jain, Robert Pollack, and Daniel Ross)
    Research in Number Theory 2:25 (2016).
  5. The shapes of pure cubic fields
    Proceedings of the American Mathematical Society 145, no. 2 (2017), pp. 509–524.
  6. Iwasawa theory for symmetric powers of CM modular forms at non-ordinary primes, II (with Jonathan Pottharst)
    Journal de Théorie des Nombres de Bordeaux 28, no. 3 (2016), pp. 655–677.
  7. Counting elliptic curves with prescribed torsion (with Andrew Snowden)
    Crelles Journal 729 (2017), pp. 151–170.
  8. On symmetric power L-invariants of Iwahori level Hilbert modular forms (with Andrei Jorza)
    American Journal of Mathematics 139, no. 6 (2017), pp. 1605–1647.
  9. Gauss–Manin connections for p-adic families of nearly overconvergent modular forms (with Liang Xiao)
    Annales de l'Institut Fourier 64, no. 6 (2014), pp. 2449–2464.
  10. Iwasawa theory for symmetric powers of CM modular forms at non-ordinary primes (with Antonio Lei)
    Journal de Théorie des Nombres de Bordeaux 26, no. 3 (2014), pp. 673–707.
  11. The exceptional zero conjecture for symmetric powers of CM modular forms: the ordinary case
    International Mathematics Research Notices 2013, no. 16, art. ID rns161, pp. 3744–3770.
  12. On Greenberg’s L-invariant of the symmetric sixth power of an ordinary cusp form
    Compositio Mathematica 148, no. 4 (2012), pp. 1033–1050.
  13. L-invariants of low symmetric powers of modular forms and Hida deformations
    PhD thesis, Princeton University, 2009.
    Advisor: Andrew Wiles.

Notes & slides

Graphics

Some data visualizations I've created. Click on an image for a description of it.

Code

You can find some of my coding projects on my GitHub account. Some of them are mentioned below.