Helena Verrill

Dr Helena Verrill

Associate Professor, with a focus on teaching and outreach/public engagement. Director of Student Experience for Maths students.

Office: B1.35
Phone: +44 (0)24 76523542
Email: H dot A dot Verrill at warwick dot ac dot uk

Teaching Responsibilities 2025/26:

Terms 1 and 2: MA3L3, Communicating Mathematics

Term 2: MA300, Cryptography

Student opportunities:

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, or helping with the Royal Institute Masterclasses.

Research Background: Number theory, modular forms, computational and algorithmic number theory / algebra, 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):

On l-adic representations for a space of noncongruence cuspforms, Jerome William Hoffman, Ling Long, and Helena Verrill, Proc. Amer. Math. Soc. 140 (2012), no. 5, 1569 - 1584, DOI 10.1090/S0002-9939-2011-11045-1. MR2869141 arXiv version.
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 Γ₁(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
Sums of squares of binomial coefficients, with applications to Picard-Fuchs equations H. A. Verrill https://arxiv.org/abs/math/0407327
Hinged Truchet tiling fractals H Verrill (October 2021) https://arxiv.org/abs/2110.01069

Published articles in recreational mathematics, combinatorial game theory, generative art:

Fractals from Trouchet Tilings, XXIV Generative Art 2021, Proceedings of XXIV GA Conference, December 2021. , pages 307-314. (see also corresponding programs here and here. )
Continuous Deformations of the Waterbomb Base Tessellation H. A. Verrill, Bridges 2021 Conference Proceedings, pages 225-232
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).

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