Third year essays, R projects and research URSS in number theory, group theory, algebraic geometry, combinatorial game theory.

Outreach projects and opportunities, either one off or ongoing, paid or unpaid, for events like Slice of Science, or outreach URSS.

Research Background: Number theory, modular forms, computational number theory, arithmetic/algebraic geometry

Other Mathematical Interest: Mathematics of origami; combinatorial game theory; combinatorics; geometry; algebra; generative art as a means of communicating mathematics

Published articles (number theory and algebraic geometry):

Infinite class of new sign ambiguities, Heon Kim, Paul van Wamelen, and Helena A. Verrill, J. Number Theory 131 (2011), no. 10, 1808-1823, DOI 10.1016/j.jnt.2011.03.005. MR2811548

Lifts of projective congruence groups, Ian Kiming, Matthias Schuett, and Helena A. Verrill, J. Lond. Math. Soc. (2) 83 (2011), no. 1, 96-120, DOI 10.1112/jlms/jdq062. MR2763946 arXiv version.

Congruences related to modular forms, H. A. Verrill, Int. J. Number Theory 6 (2010), no. 6, 1367-1390, DOI 10.1142/S1793042110003587. MR2726587

Modular forms on noncongruence subgroups and Atkin-Swinnerton-Dyer relations, Liqun Fang, J. William Hoffman, Benjamin Linowitz, Andrew Rupinski, and Helena Verrill, Experiment. Math. 19 (2010), no. 1, 1-27. MR2649983 arXiv version.

Supercongruences for the Catalan-Larcombe-French numbers, Frazer Jarvis and Helena A. Verrill, Ramanujan J. 22 (2010), no. 2, 171-186, DOI 10.1007/s11139-009-9218-5. arXiv version.

The Apery numbers, the Almkvist-Zudilin numbers and new series for 1/π, Heng Huat Chan and Helena Verrill, Math. Res. Lett. 16 (2009), no. 3, 405-420, DOI 10.4310/MRL.2009.v16.n3.a3. MR2511622

Symmetric groups and conjugacy classes, Edith Adan-Bante and Helena Verrill, J. Group Theory 11 (2008), no. 3, 371-379, DOI 10.1515/JGT.2008.021. MR2419007 arXiv version.

Computing with toric varieties, Helena Verrill and David Joyner, J. Symbolic Comput. 42 (2007), no. 5, 511-532, DOI 10.1016/j.jsc.2006.08.005. MR2322471 arXiv version.

On the modularity of Calabi-Yau threefolds containing elliptic ruled surfaces, K. Hulek and H. Verrill, Mirror symmetry. V, AMS/IP Stud. Adv. Math., vol. 38, Amer. Math. Soc., Providence, RI, 2006, pp. 19-34. With an appendix by Luis V. Dieulefait. MR2282953 arXiv version.

On the motive of Kummer varieties associated to Γ_{1}(7), Klaus Hulek and Helena A. Verrill, supplement to "The modularity of certain non-rigid Calabi-Yau threefolds", R. Livné and N. Yui, J. Math. Kyoto Univ. no. 4, J. Math. Kyoto Univ. 45 (2005), no. 4, 667-681. arXiv version.

On modularity of rigid and nonrigid Calabi-Yau varieties associated to the root lattice A4, Klaus Hulek and Helena Verrill, Nagoya Math. J. 179 (2005), 103-146, DOI 10.1017/S0027763000025617. MR2164402 arXiv version.

On modular mod l Galois representations with exceptional images, Ian Kiming and Helena A. Verrill, J. Number Theory 110 (2005), no. 2, 236-266, DOI 10.1016/j.jnt.2004.05.003. MR2122608 arXiv version.

Fundamental domains for Shimura curves, David R. Kohel and Helena A. Verrill, J. Thér. Nombres Bordeaux 15 (2003), no. 1, 205-222 (English, with English and French summaries). Les XXIIèmes Journées Arithmetiques (Lille, 2001). MR2019012

Transportable modular symbols and the intersection pairing, Helena A. Verrill, Algorithmic number theory (Sydney, 2002), Lecture Notes in Comput. Sci., vol. 2369, Springer, Berlin, 2002, pp. 219-233, DOI 10.1007/3-540-45455-1_18.

Cuspidal modular symbols are transportable, William A. Stein and Helena A. Verrill, LMS J. Comput. Math. 4 (2001), 170-181, DOI 10.1112/S146115700000084X. MR1901355

Picard-Fuchs equations of some families of elliptic curves, H. A. Verrill, Proceedings on Moonshine and related topics (Montréal, QC, 1999), CRM Proc. Lecture Notes, vol. 30, Amer. Math. Soc., Providence, RI, 2001, pp. 253-268.

The L-series of certain rigid Calabi-Yau threefolds, H. A. Verrill, J. Number Theory 81 (2000), no. 2, 310-334, DOI 10.1006/jnth.1999.2449. MR1752257

Thompson series, and the mirror maps of pencils of K3 surfaces, The arithmetic and geometry of algebraic cycles, Helena Verrill and Noriko Yui, (Banff, AB, 1998), CRM Proc. Lecture Notes, vol. 24, Amer. Math. Soc., Providence, RI, 2000, pp. 399-432. MR1738869

Arithmetic of a certain Calabi-Yau threefold, H. A. Verrill,, Number theory (Ottawa, ON, 1996), CRM Proc. Lecture Notes, vol. 19, Amer. Math. Soc., Providence, RI, 1999, pp. 333-340. MR1684614

Root lattices and pencils of varieties, J. Math. Kyoto Univ. 36 (1996), no. 2, 423-446, DOI 10.1215/kjm/1250518557. MR1411339

Preprint only:

Products of conjugacy classes of the alternating group Edith Adan-Bante, John Harris, Helena Verrill https://arxiv.org/abs/0906.2701

Paths on Three Circles, Helena Verrill Proceedings of Bridges 2020: Mathematics, Art, Music, Architecture, Education, Culture Pages 391-394

Coin-moving puzzles, Erik D. Demaine, Martin L. Demaine, and Helena A. Verrill, More games of no chance (Berkeley, CA, 2000), Math. Sci. Res. Inst. Publ., vol. 42, Cambridge Univ. Press, Cambridge, 2002, pp. 405-431. MR1973108 arXiv version.

Origami Tessellations, Bridges: Mathematical Connections in Art, Music, and Science (1998).