Jennifer S. Balakrishnan
Clare Boothe Luce Associate Professor
Department of Mathematics and Statistics
Email: jbala [at] bu.edu
Office: MCS 271
My research is in algorithmic number theory and arithmetic geometry. My work is supported by the Luce Foundation, the National Science Foundation, the Simons Foundation, and the Sloan Foundation.
I am part of the Simons Collaboration on Arithmetic Geometry, Number Theory, and Computation.
There are currently three Ph.D. students working with me.
Fall 2021: MA 841 (Greatest hits in arithmetic geometry)
Spring 2021: MA 242 (Linear algebra)
Fall 2020: MA 841 (Greatest hits in number theory)
Spring 2020: MA 124 (Calculus II)
Mathematics of Computation
Quarterly Journal of Mathematics
Journal de Théorie des Nombres de Bordeaux
Research in Number Theory
Number Theory Foundation (Board of Directors)
ICERM (Scientific Advisory Board)
Publications and preprints
- Even values of Ramanujan’s tau-function (with K. Ono and W.-L. Tsai).
- Quadratic Chabauty for modular curves: Algorithms and examples (with N. Dogra, J. S. Müller, J. Tuitman, J. Vonk).
- Variants of Lehmer's speculation for newforms (with W. Craig, K. Ono, W.-L. Tsai).
- Variations of Lehmer's Conjecture for Ramanujan's tau-function (with W. Craig, K. Ono), to appear, Journal of Number Theory (Special issue – New developments in the theory of modular forms over function fields).
- Computational tools for quadratic Chabauty (with J. S. Müller; draft lecture notes for 2020 Arizona Winter School, will be updated periodically).
- Two recent p-adic approaches towards the (effective) Mordell conjecture (with A. J. Best, F. Bianchi, B. Lawrence, J. S. Müller, N. Triantafillou, J. Vonk), to appear, Arithmetic L-functions and differential geometric methods, 2021, 31-74.
- Explicit quadratic Chabauty over number fields (with A. Besser, F. Bianchi, J. S. Müller), Israel Journal of Mathematics, (2021), 1-48.
- What is...a Coleman integral?, Notices of the AMS, 66, no. 5 (2019), 738-740.
Chabauty-Coleman experiments for genus 3 hyperelliptic curves (with F. Bianchi, V. Cantoral-Farfán, M. Çiperiani, A. Etropolski), Research Directions in Number Theory, Association for Women in Mathematics Series, Vol. 19, Springer, 2019, 67–90.
- An effective Chabauty-Kim theorem (with N. Dogra), Compositio Mathematica, 155, no. 6 (2019), 1057–1075.
- Explicit Chabauty-Kim for the split Cartan modular curve of level 13 (with N. Dogra, J. S. Müller, J. Tuitman, J. Vonk), Annals of Mathematics,
189, No. 3 (May 2019), 885-944.
- Explicit Coleman integration for curves (with J. Tuitman), Mathematics of Computation, 89 (2020), 2965–2984.
- Quadratic Chabauty and rational points II: Generalised height functions on Selmer varieties (with N. Dogra), International Mathematics Research Notices, (2020), rnz362.
- Quadratic Chabauty and rational points I: p-adic heights (with N. Dogra and an appendix by J. S. Müller), Duke Mathematical Journal, 167, no. 11 (2018), 1981-2038.
- Constructing genus 3 hyperelliptic Jacobians with CM (with S. Ionica, K. Lauter, C. Vincent), LMS Journal of Computation and Mathematics 19 Issue A (Algorithmic Number Theory Symposium XII), (2016), 283-300.
- Databases of elliptic curves ordered by height and distributions of Selmer groups and ranks (with W. Ho, N. Kaplan, S. Spicer, W. Stein, J. Weigandt), LMS Journal of Computation and Mathematics 19 Issue A (Algorithmic Number Theory Symposium XII), (2016), 351-370.
- Computing integral points on hyperelliptic curves using quadratic Chabauty (with A. Besser, J. S. Müller), Mathematics of Computation 86 (2017), 1403-1434.
- Shadow lines in the arithmetic of elliptic curves (with M. Çiperiani, J. Lang, B. Mirza, R. Newton), Directions in Number Theory: Proceedings of the WIN3 Workshop, Springer, 2016, 33-55.
- Explicit p-adic methods for elliptic and hyperelliptic curves, Advances on Superelliptic Curves and their Applications, IOS Press, 2015, 260-285.
- Quadratic Chabauty: p-adic height pairings and integral points on hyperelliptic curves (with A. Besser, J. S. Müller), Journal für die reine und angewandte Mathematik, 720 (2016), 51-79.
- A p-adic analogue of
the conjecture of Birch and Swinnerton-Dyer for modular abelian
varieties (with J. S. Müller, W. Stein), Mathematics of Computation, 85 (2016), 983-1016.
- A non-abelian conjecture of Tate-Shafarevich type for hyperbolic curves
(with I. Dan-Cohen, M. Kim, S. Wewers), Mathematische Annalen, 372(2018), no. 1-2, 369-428.
- On 3-adic heights on elliptic curves, Journal of Number Theory (Special issue - in honor of Wen-Ching Winnie Li), 161 (2016), 119-134.
- Coleman integration for even degree models of hyperelliptic curves, LMS Journal of Computation and Mathematics, 18 (2015), 258-265.
- p-adic heights of
Heegner points and Lambda-adic regulators (with
M. Çiperiani, W. Stein), Mathematics of Computation, 84 (2015), 923-954.
- Comparing arithmetic intersection formulas for
denominators of Igusa class polynomials (with J. Anderson,
K. Lauter, J. Park, B. Viray), Women in Numbers 2: Research Directions in Number Theory, Contemporary Mathematics, 606, AMS, 2013, 65-82.
- Coleman-Gross height pairings
and the p-adic sigma function (with A. Besser), Journal für die reine und angewandte Mathematik, 698 (2015), 89-104.
- Iterated Coleman integration for hyperelliptic curves, ANTS-X: Proceedings of the Tenth Algorithmic Number Theory Symposium, Open Book Series 1, MSP, 2013, 41-61.
local p-adic height pairings on hyperelliptic curves (with
A. Besser), International Mathematics Research Notices
(2012) 2012 (11): 2405-2444. (Errata)
- Appendix and erratum to Minhyong Kim, "Massey products for elliptic curves of rank 1" (with K. Kedlaya, M. Kim), Journal of the American Mathematical Society 24 (2011), 281-291.
- Pairings on hyperelliptic curves (with J. Belding, S. Chisholm, K. Eisentraeger, K. Stange, E. Teske), WIN - Women in Numbers, Fields Institute Communications, 60, AMS, 2011, 87-120.
- Explicit Coleman integration for hyperelliptic curves (with R. Bradshaw, K. Kedlaya), Algorithmic Number Theory (ANTS-IX), LNCS 6197, Springer, 2010, 16-31.
Recent and Upcoming Events
Diophantine Geometry, Spring 2023 at MSRI, co-organized with Mirela Çiperiani, Philipp Habegger, Wei Ho, Hector Pasten, Yunqing Tang, Shou-Wu Zhang
Park City Mathematics Institute 2022: Number Theory Informed by Computation, July 17 - August 6, 2022, Park City, co-organized with Bjorn Poonen and Akshay Venkatesh
GirlsGetMath at BU (for high school students), 2022 at Boston University, co-organized with Margaret Beck
(Virtual) Park City Mathematics Institute 2021 Graduate Summer School (Week 3: Number Theory Informed by Computation), July 26 - 30, 2021, co-organized with Bjorn Poonen and Akshay Venkatesh
Rational Points and Galois Representations, May 10 - 12, 2021, co-organized with Netan Dogra and Carl Wang-Erickson, with JSB and Brian Lawrence as scientific organizers
Connecticut Summer School and Conference in Number Theory, June 8 - 14, 2020, co-organized with Keith Conrad, Álvaro Lozano-Robledo, and Christelle Vincent
Boston University-Keio University workshop 2019, June 24 - 28, 2019 at Boston University, co-organized with Ali Altug, Steve Rosenberg, and Kenichi Bannai
CMI-HIMR Summer School in Computational Number Theory, June 17 - 28, 2019 at the University of Bristol, co-organized with Tim Dokchitser
Arithmetic of Low-Dimensional Abelian Varieties, June 3 - 7, 2019 at ICERM, co-organized with Noam Elkies, Brendan Hassett, Bjorn Poonen, Andrew Sutherland, and John Voight
Arithmetic Geometry, Number Theory, and Computation, August 20 - 24, 2018 at MIT, co-organized with Noam Elkies, Brendan Hassett, Bjorn Poonen, Andrew Sutherland, and John Voight
WIN4: Women in Numbers 4, August 13 - 18, 2017 at the Banff International Research Station, co-organized with Chantal David, Michelle Manes, and Bianca Viray
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