Max Planck Institute for Mathematics in the Sciences
sachi.hashimoto [at] mis [dot] mpg [dot] de
Office: F3 13
I am broadly interested in number theory and algebraic geometry. More specifically, I am interested in rational points and explicit methods in arithmetic geometry.
- Self-dual matroids from canonical curves (with Alheydis Geiger, Bernd Sturmfels, and Raluca Vlad), arXiv:2212.05910.
- Geometric quadratic Chabauty and p-adic heights (with Juanita Duque-Rosero and Pim Spelier), arXiv:2207.10389.
- Quadratic Chabauty and p-adic Gross-Zagier, to appear, Transactions of the American Mathematical Society.
- A geometric linear Chabauty comparison theorem (with Pim Spelier), Acta Arithmetica 202 (2022), no. 1, 67–88. 11G30 (11D45).
- A transcendental Brauer-Manin obstruction to weak approximation on a Calabi-Yau threefold (with Katrina Honigs, Alicia Lamarche, and Isabel Vogt, and an appendix by Nicolas Addington),
Research in Number Theory 8 (2022), no. 1, Paper No. 12.
38406501359372282063949 & all that: Monodromy of Fano Problems (with Borys Kadets), International Mathematics Research Notices (2020), rnaa275.
- Chabauty-Coleman computations on rank 1 Picard curves (with Travis Morrison), Arithmetic Geometry, Number Theory, and Computation, Simons Symposia, Springer, 2021, 485-506.
- Computing rational points on rank 0 genus 3 hyperelliptic curves (with María Inés de Frutos-Fernández), Arithmetic Geometry, Number Theory, and Computation, Simons Symposia, Springer, 2021, 449-460.
Here are some expository notes on the geometric quadratic Chabauty theory of Edixhoven and Lido.
Teaching and Outreach
- Directed Reading Program at Boston University, co-founder and co-director, 2018 - 2022
- Proof School, 2015-2017, middle and high school teacher
- Canada/USA Mathcamp, summers 2014, 2015, 2016, 2019
- Love Math!, a festival for girls, co-founder and co-director, 2016 - 2019.