Mathematics

Publications and Preprints:

  1. The Gelfand-Graev representation of GSp(4, Fq) (with Julianne Rainbolt), Comm. Algebra 47 (2019), no. 2, pp. 560-584. DOI: 10.1080/00927872.2018.1485228, (pdf) 2016: (online journal 1) 2019: (online journal 2)
  2. Computations of spaces of paramodular forms of general level (with Cris Poor and David S. Yuen), J. Korean Math. Soc. 53 (2016), no. 3, pp. 645-689. (pdf) (journal)
  3. Irreducible characters of GSp(4,q) and dimensions of spaces of fixed vectors, Ramanujan J. 36 (2015), no. 3, pp. 305-354. (pdf) (journal)
  4. Irreducible non-cuspidal characters of GSp(4,Fq), Ph.D. Thesis, University of Oklahoma, 2011. 145 pp. (pdf)

Computer Algebra Systems:

  1. Sage: a free open-source mathematics software system licensed under the GPL. It builds on top of many existing open-source packages: NumPy, SciPy, matplotlib, Sympy, Maxima, GAP, FLINT, R and many more. Access their combined power through a common, Python-based language or directly via interfaces or wrappers.
  2. CoCalc: Collaborative Calculation in the Cloud
  3. Magma: a large, well-supported software package designed for computations in algebra, number theory, algebraic geometry and algebraic combinatorics.

Code:

  1. Computing theta blocks: A Python package and a Jupyter notebook for computing spaces of Jacobi cusp forms using the theory of theta blocks

Links:

  1. LMFDB.org: an extensive database of mathematical objects arising in Number Theory.
  2. GSp4.org: a freely accessible database about the existing literature on GSp(4).
  3. SiegelModularForms.org: Siegel modular forms computations.
  4. Siegel Modular Forms of Degree 2 and 3: an open access source for information on traces of Hecke operators on Siegel modular forms of degree 2, level 1 and level 2, and of degree 3, level 1.
  5. MathSciNet
  6. Number Theory Conferences New and Old
  7. Number Theory on the arXiv
  8. Representation Theory on the arXiv
  9. Algebraic Geometry on the arXiv
  10. The Mathematics Genealogy Project
© 2019 Jeff Breeding-Allison