Department of Mathematics and Statistics

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Office: Petty 146
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Ph.D. in Mathematics, Duke University (2005)

Member of the UNCG Number Theory Group.
Upcoming: Summer School in Computational Number Theory 2017: Modular Forms.

Information about teaching can be found in the menu to the left.

Publications and Preprints

Links below are to published versions and PDF preprint version.

1. Perfect forms over CM quartic fields (extended abstract), Mathematisches Forschungsinstitut Oberwolfach, Report No. 3/2016, Lattices and Applications in Number Theory. (PDF)
2. with Andrew R. Booker, Jeroen Sijsling, Andrew V. Sutherland, and John Voight, A database of genus 2 curves over the rational numbers, LMS J. Comput. Math. 19 (2016), no. suppl. A, 235–254. (PDF)
3. with Steve Donnelly, Paul E. Gunnells, and Ariah Klages-Mundt, A table of elliptic curves over the cubic field of discriminant -23, Experimental Mathematics, 24:4 (2015), 375-390. (PDF)
4. with Mathieu Dutour Sikirić, Herbert Gangl, Paul E. Gunnells, Jonathan Hanke, and Achille Schürmann, On K_4 of the Gaussian and Eisenstein Integers, submitted. (PDF)
5. with Mathieu Dutour Sikirić, Herbert Gangl, Paul E. Gunnells, Jonathan Hanke, and Achille Schürmann, On the cohomology of linear groups over imaginary quadratic fields, Journal of Pure and Applied Algebra 220, Issue 7, July 2016, 2564–2589. (PDF)
6. Integral cohomology of certain Picard modular surfaces, J. Number Theory 134 (2014) 13-28. (PDF)
7. Perfect unary forms over real quadratic fields, J. Théor Nombres Bordeaux 25 (2013), no. 3, 759-775. (PDF)
8. with Paul E. Gunnells, Modular forms and elliptic curves over the cubic field of discriminant −23, Int. J. Number Theory 9 (2013), no. 1, 53-76. (PDF)
9. Computing modular forms for GL_2 over certain number fields, Computations with Modular Forms, Contributions in Mathematical and Computational Sciences 6 (2014), 363-377.
10. with Farshid Hajir and Paul E. Gunnells, Modular forms and elliptic curves over the field of fifth roots of unity, Exp. Math. 22 (2013), no. 2, 203-216. (PDF)
11. Computing modular forms using Voronoi polyhedra (extended abstract), Mathematisches Forschungsinstitut Oberwolfach, Report No. 35/2011, Explicit Methods in Number Theory. (PDF)
12. On modular forms and elliptic curves over $\mathbb{Q}(\zeta_5)$, RIMS Automorphic forms, trace formulas, and zeta functions (2011), Proceedings. (PDF)
13. with Adriano Bruno, The arithmetic of planar binary trees, Involve 4 (2011), no. 1, 1-11. (PDF)
14. Hyperbolic tessellations associated to Bianchi groups, 6197 (2010), 385 - 396, 9th International Symposium, Nancy, France, ANTS-IX, July 19-23, 2010, Proceedings. (PDF)
15. Binary Hermitian forms over a cyclotomic field, J. Algebra 322 (2009), 4132-4142. (PDF)
16. Computing Hecke operators on Bianchi forms, Tech. Report, Magma computational group: University of Sydney, 2009. (PDF)
17. Modular forms over imaginary quadratic fields, package available in Magma V2.16, 2009.
18. with Paul E. Gunnells, Hecke operators and Hilbert modular forms, Algorithmic number theory, Lecture Notes in Comput. Sci., vol. 5011, Springer, Berlin, 2008, pp. 387-401. (PDF)
19. Elliptic points of the Picard modular group, Monatsh. Math. (2009), no. 156, 391-396. (PDF)
20. An explicit spine for the Picard modular group over the Gaussian integers, J. Number Theory 128 (2008), no. 1, 207-234. (PDF)
21. On the existence of spines for $\mathbb{Q}$-rank 1 groups, Selecta Math. (N.S.) 12 (2006), no.3-4, 541-564. (PDF)
22. On the existence of spines for $\mathbb{Q}$-rank 1 groups, Ph.D. Thesis, Duke University, 2005.