Email: jennifer.balakrishnan [at] maths.ox.ac.uk Office: N1.24, Mathematical Institute, Oxford | ||
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**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**

- Constructing genus 3 hyperelliptic Jacobians with CM (with S. Ionica, K. Lauter, C. Vincent).
- 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.
- Quadratic Chabauty and rational points I:
*p*-adic heights (with N. Dogra and an appendix by J. S. Müller). - Computing integral points on hyperelliptic curves using quadratic Chabauty (with A. Besser, J. S. Müller), to appear in
*Mathematics of Computation*. - 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*. - 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), to appear in*Journal für die reine und angewandte Mathematik*. - 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 Birch and Swinnerton-Dyer type for hyperbolic curves (with I. Dan-Cohen, M. Kim, S. Wewers).
- 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**

Past students:

- Michelle Kovesi, Proving the weak BSD conjecture for elliptic curves in the Cremona database, MSc 2015.
- Bo Schmidt, Solutions to systems of multivariate
*p*-adic power series, MSc 2015. - Charlene Soh, Explicit methods for the Birch and Swinnerton-Dyer conjecture, MSc 2014.
- Haikal Yeo, Computations motivated by the
*p*-adic Birch and Swinnerton-Dyer conjecture, MSc 2014. - John Musson, Bounded gaps between consecutive primes, MMath 2015.
- Samuel Porritt,
*p*-adic analysis and rational points on curves, MMath 2015. - Florence Walton, The congruent number problem and the Birch and Swinnerton-Dyer conjecture, MMathPhil, 2015.

Teaching in past terms:

- Trinity Term 2015: Lecturer, Part A Number theory and consultation sessions for B3.4 Algebraic number theory
- Hilary Term 2015: Class tutor for B3.4 Algebraic number theory
- Michaelmas Term 2014: Class tutor for B3.1 Galois theory
- Trinity Term 2014: Consultation sessions for B9b Algebraic number theory and C9.1b Elliptic curves
- Hilary Term 2014: Class tutor for B9b Algebraic number theory and C9.1b Elliptic curves
- Michaelmas Term 2013: College tutor for Analysis I (Sequences and series) and Algebra 1 (Linear algebra), Brasenose College

**Links**

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