Jennifer S. Balakrishnan

Email: jennifer.balakrishnan [at] maths.ox.ac.uk

Office: N1.24, Mathematical Institute, Oxford

About me

I am a Titchmarsh Research Fellow at the Mathematical Institute of the University of Oxford and a Junior Research Fellow at Balliol College.

I received my PhD from MIT in June 2011, under the direction of Kiran Kedlaya. Here is my CV.

Publications and preprints

  1. Constructing genus 3 hyperelliptic Jacobians with CM (with S. Ionica, K. Lauter, C. Vincent).
  2. 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). The databases may be accessed here.
  3. Quadratic Chabauty and rational points I: p-adic heights (with N. Dogra and an appendix by J. S. Müller).
  4. Computing integral points on hyperelliptic curves using quadratic Chabauty (with A. Besser, J. S. Müller), to appear in Mathematics of Computation.
  5. Shadow lines in the arithmetic of elliptic curves (with M. Çiperiani, J. Lang, B. Mirza, R. Newton), to appear in Directions in Number Theory: Proceedings of the WIN3 Workshop.
  6. Explicit p-adic methods for elliptic and hyperelliptic curves, Advances on Superelliptic Curves and their Applications, IOS Press, 2015, 260-285.
  7. Quadratic Chabauty: p-adic height pairings and integral points on hyperelliptic curves (with A. Besser, J. S. Müller), to appear in Journal für die reine und angewandte Mathematik.
  8. 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.
  9. A non-abelian conjecture of Birch and Swinnerton-Dyer type for hyperbolic curves (with I. Dan-Cohen, M. Kim, S. Wewers).
  10. On 3-adic heights on elliptic curves, Journal of Number Theory (Special issue - in honor of Wen-Ching Winnie Li), 161 (2016), 119-134.
  11. Coleman integration for even degree models of hyperelliptic curves, LMS Journal of Computation and Mathematics, 18 (2015), 258-265.
  12. p-adic heights of Heegner points and Lambda-adic regulators (with M. Çiperiani, W. Stein), Mathematics of Computation, 84 (2015), 923-954.
  13. 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.
  14. Coleman-Gross height pairings and the p-adic sigma function (with A. Besser), Journal für die reine und angewandte Mathematik, 698 (2015), 89-104.
  15. Iterated Coleman integration for hyperelliptic curves, ANTS-X: Proceedings of the Tenth Algorithmic Number Theory Symposium, Open Book Series 1, MSP, 2013, 41-61.
  16. Computing local p-adic height pairings on hyperelliptic curves (with A. Besser), International Mathematics Research Notices (2012) 2012 (11): 2405-2444.
  17. 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.
  18. 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.
  19. Explicit Coleman integration for hyperelliptic curves (with R. Bradshaw, K. Kedlaya), Algorithmic Number Theory (ANTS-IX), LNCS 6197, Springer, 2010, 16-31.

Teaching

I am currently supervising four Part C dissertations in Mathematics.

Past students:

Teaching in past terms:

Links

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 Days 69: Women in Sage 6, September 4 - 9, 2015 in San Diego, co-organized with Aly Deines
Sage Days 68: Bug Days, August 21 - 27, 2015 in Samish Island, co-organized with Aly Deines and William Stein
Sage Days 64.25: Bug Days, May 23 - 27, 2015 in San Diego, co-organized with Aly Deines and William Stein
It all adds up: celebrating women across the mathematical sciences, April 14 - 17, 2015 at the University of Oxford
NATO ASI 2014: Arithmetic of Hyperelliptic Curves, August 25 - September 5, 2014 in Ohrid, Macedonia (FYROM)
Sage Days 56: Computational number theory and the cloud, January 2 - 7, 2014 in Honolulu, co-organized with Aly Deines and William Stein
Computational number theory, geometry, and physics (Sage Days 53), September 23 - 29, 2013 at the University of Oxford, co-organized with Volker Braun
Sage Days 50: Women in Sage (4), July 10 - 15, 2013 in Seattle, co-organized with Aly Deines
Sage Days 46: Computational number theory, February 26 - March 2, 2013 in Honolulu, co-organized with Aly Deines, Xander Faber, Michelle Manes, and William Stein
Arithmetic statistics, January 10, 2013 at the Joint Mathematics Meetings in San Diego, co-organized with Kevin McGown and Ethan Smith
Sage Days 42: Women in Sage (3), July 15-19, 2012 in Seattle, co-organized with Aly Deines and Lola Thompson
Rational points on varieties, January 5-6, 2012 at the Joint Mathematics Meetings in Boston, co-organized with Bjorn Poonen, Bianca Viray, and Kirsten Wickelgren
Sage Days 33: Women in Sage (2), September 19-23, 2011 in Seattle, co-organized with Aly Deines and William Stein

Galois Visualizations, a program written with Vivek Venkatachalam, in consultation with Minhyong Kim, James Haydon, and Jan Vonk (program guide)
Sage, free, open-source mathematical software