Scholarship

My research is in the general area of Number Theory. I obtained my Ph.D. in 2009 at the University of Texas at Austin under the direction of Fernando Rodriguez-Villegas, and the title of my thesis was “Hypergeometric Functions in Arithmetic Geometry.” I am working on several projects at the moment: in the theory of formal multizeta values, arithmetic dynamics, arithmetic mirror symmetry, and mathematical origami. 

I am a proud member of the Women in Number Theory group, and  you will notice that many of the publications listed below are closely tied with this wonderful research community. 

Publications and Preprints

1.  Grassmannian arrow pencils and Hasse-Witt invariants, with Ursula Whitcher and Chenglong Yu, submitted. 

2. Higher dimensional origami constructions, with Deveena Banerjee and Sara Chari, Involve, Vol. 16 (2023), No. 2, 297–312. 

3. Hasse-Witt matrices and mirror toric pencils, with Ursula Whitcher, Advances in Theoretical and Mathematical Physics, Vol. 26, No. 9 (2022), pp. 3345-3375.  

4. Mould theory and the double shuffle Lie algebra structure, with Leila Schneps, Periods in Quantum Field Theory and Arithmetic (Burgos Gil, Ebrahimi-Fard, Gangl, eds.), Springer Proceedings in Mathematics & Statistics, 2020.  arXiv:1510.05535. 

5. Hypergeometric decomposition of symmetric K3 quartic pencils, with Charles Doran, Tyler Kelly, Steven Sperber, John Voight, and Ursula Whitcher, Research in the Mathematical Sciences 7, 7 (2020). (Published online March 16, 2020.) 

6. Integrality properties of Bötcher coordinates for one-dimensional superattracting germs, with Joseph H. Silverman,  Ergodic Theory and Dynamical Systems , Vol. 40, No. 1 (2020),  248-271 . (Published online July 6, 2018.) arXiv:1708.09275 

7. Zeta functions of alternate mirror Calabi-Yau families, with Charles Doran, Tyler Kelly, Steven Sperber, John Voight, and Ursula Whitcher, Israel Journal of Mathematics 228 (2018), no. 2, 665-705. arXiv:1612.09249. 

8. Origami constructions of the ring of integers of an imaginary quadratic field, with Jürgen Kritschgau,  INTEGERS,  Vol. 17,  #A34. 

9. Symmetries of rational functions arising in Ecalle's study of multiple zeta values, with Damaris Schindler and Amanda Tucker, Women in Numbers Europe: Research Directions in Number Theory,  Association for Women in Mathematics Series 2, Springer, 2015, 153--166.  (PDF )

10. An Algorithmic Approach to the Dwork Family, in Women in Numbers 2, Contemporary Mathematics, vol. 606, Amer. Math. Soc., Providence, RI, 2013, 83 --100.  (PDF)

11. Counting Points over Finite Fields and Hypergeometric Functions, Funct. Approx. Comment. Math., Vol. 49, No. 1 (2013), 137--157. (PDF)

12. Igusa class polynomials, embeddings of quartic CM fields, and arithmetic intersection theory, with Helen Grundman, Jennifer Johnson-Leung, Kristin Lauter, Bianca Viray, and Erika Wittenborn.  WIN -- Women in Numbers, Fields Institute Communications, vol. 60, Amer. Math. Soc., Providence, RI, 2011,  35 -- 60.  (PDF)

Reports and extended abstracts

1. Alternate mirror families and Hypergeometric Motives (extended abstract), with Charles Doran, Tyler Kelly, Steven Sperber, John Voight, and Ursula Whitcher , to appear in Springer volume for the MATRIX Institute Book Series. 

2. Arithmetic, Hypergeometric Functions, and Mirror Symmetry (summary of a talk I gave, written by Marine Rougnant), based on work with Charles Doran, Tyler Kelly, Steven Sperber, John Voight, and Ursula Whitcher,  Proceedings of the Fourth Mini Symposium of the Roman Number Theory Association, held April 18-20, 2018.