Research

My research is in arithmetic algebraic geometry, an area at the intersection of number theory and algebraic geometry. I am also interested in computational aspects of number theory, algebraic geometry, representation theory, and other algebraic topics.

ORCID page

Preprints (in preparation)

Preprints (submitted)

Publications

  1. Distinguishing newforms (with S. Chow), International Journal of Number Theory 11, no. 3 (2015), 893-908. (arXiv copy) Sage source code and data
  2. Distinguishing eigenforms modulo a prime ideal (with S. Chow), Functiones et Approximatio Commentarii Mathematici 51, no. 2 (2014), 363-377. (arXiv copy)
  3. Hecke eigenvalues of Siegel modular forms of ''different'' weights (with R. Sayer), Journal of Number Theory 143, no. 10 (2014), 125-141. (arXiv copy)
  4. Computing level one Hecke eigensystems (mod p) (with C. Citro), LMS Journal of Computation and Mathematics 16 (2013), 246-270. (arXiv copy)
  5. Computations of vector-valued Siegel modular forms (with N. Ryan and D. Sulon), Journal of Number Theory 133, no. 11 (2013), 3921-3940. (arXiv copy)
  6. Experimental evidence for Maeda's conjecture on modular forms (with A. McAndrew), Tbilisi Mathematical Journal 5, no. 2 (2012), 55-69, special issue on symbolic computation using Sage. (arXiv copy)
  7. Distinguishing Hecke eigenforms, International Journal of Number Theory 7, no. 5 (2011), 1247-1253. (arXiv copy)
  8. Enumerating Galois representations in Sage (with C. Citro), in K. Fukuda et al (Eds), Proceedings of the International Congress on Mathematical Software 2010, Lecture Notes in Computer Science 6327 (2010), 256-259, Springer, Heidelberg. (arXiv copy)
  9. All Siegel Hecke eigensystems (mod p) are cuspidal, Mathematical Research Letters 13, no. 5-6 (2006), 813-823. (arXiv copy)
  10. Upper bound on the number of systems of Hecke eigenvalues for Siegel modular forms (mod p), International Mathematics Research Notices, no. 55 (2004), 2983-2987. (arXiv copy)
  11. Hecke eigenvalues of Siegel modular forms (mod p) and of algebraic modular forms, Journal of Number Theory 106, no. 2 (2004), 345-384. (arXiv copy)

Erdős number 3: Erdős-Pomerance-Ryan-Ghitza

Other

Students (alphabetical)

Past students (inverse chronological)

Seminars, conferences

Talks (relatively recent)

2015
2014
2013
2012
2011
2010
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2008