Jennifer S. Balakrishnan
Clare Boothe Luce Assistant Professor
Department of Mathematics and Statistics
Boston University
CV
Email: jbala [at] bu.edu
Office: MCS 238
My research is in algorithmic number theory and arithmetic geometry. My work is supported by the Luce Foundation , the National Science Foundation and the Simons Foundation .
I am part of the Simons Collaboration on Arithmetic Geometry, Number Theory, and Computation .
There are currently five Ph.D. students working with me.
Publications and preprints
Chabauty-Coleman experiments for genus 3 hyperelliptic curves (with F. Bianchi, V. Cantoral-Farfán, M. Çiperiani, A. Etropolski), Research Directions in Number Theory: Women in Numbers IV , to appear.
An effective Chabauty-Kim theorem (with N. Dogra).
Explicit Chabauty-Kim for the split Cartan modular curve of level 13 (with N. Dogra, J. S. Müller, J. Tuitman, J. Vonk).
Explicit Coleman integration for curves (with J. Tuitman).
Quadratic Chabauty and rational points II: Generalised height functions on Selmer varieties (with N. Dogra).
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 , to appear.
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.
Computing
local p -adic height pairings on hyperelliptic curves (with
A. Besser), International Mathematics Research Notices
(2012) 2012 (11): 2405-2444.
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.
Teaching
Spring 2019: MA 124 (Calculus II)
Spring 2018: MA 242 (Linear algebra)
Fall 2017: MA 123 (Calculus I)
Spring 2017: MA 842 (Explicit methods for elliptic and hyperelliptic curves)
Links
CMI-HIMR Summer School in Computational Number Theory , June 17 - 28, 2019, at the University of Bristol, co-organized with Tim Dokchitser.
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.
Connecticut Summer School in Number Theory , May 28 - June 3, 2018, at UConn, co-organized with Keith Conrad, Álvaro Lozano-Robledo, and Liang Xiao.
Sage Days: Opening Workshop for a Year of Coding Sprints , August 21 - 25, 2017, at the IMA, co-organized with Benjamin Brubaker, Matthias Koeppe, and Gregg Musiker
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
Sage Days 87: p-adics in Sage and the LMFDB , July 17 - 22, 2017, Vermont, co-organized with Xavier Caruso, Edgar Costa, Taylor Dupuy, David Roe, William Stein, and Christelle Vincent
Women in Sage (Sage Days 82) , January 9 - 13, 2017, Paris, co-organized with Viviane Pons and Jessica Striker
Explicit p -adic methods in number theory (Sage Days 71) , March 20 - 24, 2016 at the University of Oxford, co-organized with David Roe
Sage , free, open-source mathematical software