Solving the problem of the cursed curve defined by the modular curve Xs(13) involved proving that seven known rational points were the only solutions to a complex Diophantine equation. Jennifer Balakrishnan led the team that settled this case, applying a method involving Selmer varieties to conclude a long-standing inquiry into Galois representations of elliptic curves.
Academic Foundation
Born in Mangilao, Guam, Balakrishnan developed an interest in mathematics early, earning recognition at the Intel International Science and Engineering Fair in 2001. She attended Harvard University, where she completed both a bachelor's degree magna cum laude and a master's degree in 2006. She subsequently moved to the Massachusetts Institute of Technology for doctoral studies, graduating with a Ph.D. in 2011. Her dissertation, supervised by Kiran Kedlaya, explored Coleman integration for hyperelliptic curves.
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Balakrishnan maintains a primary focus on arithmetic geometry and algorithmic number theory. In 2017, she and her co-authors utilized a Selmer variety, a method suggested by Minhyong Kim, to confirm the completeness of solutions for the cursed curve. The team proved that the seven solutions identified by previous researchers were exhaustive. Her work also extends to implementation, contributing number-theoretical algorithms to the SageMath computer algebra system and investigating Lehmer’s question regarding the Ramanujan tau function.
Professional Appointments
Following her doctoral work, she held a postdoctoral position at Harvard University from 2011 to 2013. She then moved to the University of Oxford as a Junior Research Fellow at Balliol College and a Titchmarsh Research Fellow at the Mathematical Institute. Since 2016, she has served on the faculty at Boston University, advancing from Assistant Professor to Associate Professor in 2021 and Clare Boothe Luce Professor in 2023.
Professional Service and Recognition
Balakrishnan serves on the board of directors for the Number Theory Foundation and contributes to the editorial boards of Research in Number Theory and Mathematics of Computation. She is a principal investigator in the Simons Collaboration on Arithmetic Geometry, Number Theory, and Computation. In 2022, she was named a Fellow of the American Mathematical Society, following her receipt of the AWM–Microsoft Research Prize in Algebra and Number Theory.
Fast facts
- Born: 2000
- Citizenship: United States
- Alma Mater: Harvard University, Massachusetts Institute of Technology
- Current Position: Clare Boothe Luce Professor, Boston University
- Major Contribution: Resolution of the Xs(13) cursed curve equation
- AMS Fellow: 2022
- AWM Fellow: 2023
Questions readers ask
What is the cursed curve?
It is a specific modular curve, Xs(13), characterized by a high-degree Diophantine equation. Solving it required proving that seven identified points were the only possible rational solutions.
What is her primary research methodology?
She specializes in algorithmic number theory and arithmetic geometry, often using Selmer varieties and computational methods to find rational points on algebraic curves.
Achievements
- Held posts at Boston University
- Fields: mathematics
