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For reprints (or rather electronic reprints), just shoot me an email.
9. 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). (arXiv) (GitHub)
8. The shapes of pure cubic fields
 Proceedings of the American Mathematical Society 145, no. 2 (2017), pp. 509–524. (arXiv)
7. Iwasawa theory for symmetric powers of CM modular forms at non-ordinary primes, II (with Jonathan Pottharst)
 To appear in Journal de Théorie des Nombres de Bordeaux. (arXiv)
6. Counting elliptic curves with prescribed torsion (with Andrew Snowden)
 To appear in Crelles Journal. (arXiv)
5. On symmetric power L-invariants of Iwahori level Hilbert modular forms (with Andrei Jorza)
 To appear in the American Journal of Mathematics. (arXiv)
4. 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. (arXiv)
3. 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. (arXiv)
2. 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. (arXiv)
1. On Greenberg’s L-invariant of the symmetric sixth power of an ordinary cusp form
 Compositio Mathematica 148, no. 4 (2012), pp. 1033–1050. (arXiv)
 Note: The published version contains a sketch of the proof of Theorem 3.1.
0.L-invariants of low symmetric powers of modular forms and Hida deformations
PhD thesis, Princeton University, 2009.
Advisor: Andrew Wiles.

Notes & slides

• Equidistribution of shapes of cubic fields of fixed quadratic resolvent
  These are (expanded) slides from a 15-minute talk at CNTA XIV discussing my (upcoming) paper on the equidistribution of shapes of complex cubic fields with fixed trace-zero form on the corresponding geodesics in the modular curve. (The animations don't work in Preview on Mac.)
• Critical integers of motivic L-functions and Hodge numbers
  This short note explains how to relate the critical integers of a motivic L-function (in the sense of Deligne) to the Hodge numbers of the motive. Specific examples are worked out (the Tate motive Q(1) and symmetric powers of modular forms).

Graphics

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

Cubic shapes animation Congruences of modular forms

Code

• Overconvergent modular symbols code (including Hida theory): in progress
  This code is available here on github. See the arXiv.
• Iterate factorization trees:
  This code is available here on github. It was first written at the AIM workshop on the Galois theory of orbits in arithmetic dynamics and computes the trees described in Section 3 of Rafe Jones and Nigel Boston's Settled polynomials over finite fields.
• Shape of a number field:
  This code is available here on github. It computes the "shape" of a number field. The shape of a number field K of degree n is the (n−1)-dimensional lattice in the Minkowski space given by the orthogonal complement of the vector 1. The output of this function is simply the (not necessarily reduced) Gram matrix of the lattice.
• Artin representations in Sage: in progress
  This code is available here on github. The goal of this project is to be able to compute with Artin representations in Sage. Some highlights include Artin conductors, L-functions, and root numbers. The project also improves the Galois group code to allow non-Galois fields.

Data

• Quartic CM fields: up to discriminant 1×106
  CM_fields_degree_4.sobj, a Sage object containing the embedding of the maximal totally real subfield into the quartic CM field.
  CM_fields_degree_4.txt, a text file containing data in the form of the pari group's nftables, i.e each line contains a 4-tuple whose entries are the discriminant, the coefficients of the defining polynomial, the class number, and the elementary divisors of the class group.
• Sextic CM fields: up to discriminant 2×105 (there's only 4 of them!)
  CM_fields_degree_6.sobj, a Sage object containing the embedding of the maximal totally real subfield into the quartic CM field.
  CM_fields_degree_6.txt, a text file containing data in the form of the pari group's nftables, i.e each line contains a 4-tuple whose entries are the discriminant, the coefficients of the defining polynomial, the class number, and the elementary divisors of the class group.