Sachi Hashimoto

Tamarkin Assistant Professor
Brown University
sachi_hashimoto at brown dot edu
Office: Kassar 310


I am broadly interested in number theory and algebraic geometry. More specifically, I am interested in rational points and explicit methods in arithmetic geometry.

  1. Local heights on hyperelliptic curves and quadratic Chabauty (with L. Alexander Betts, Juanita Duque-Rosero, and Pim Spelier), arXiv:2401.05228.
  2. Towards a Classification of Isolated j-invariants (with Abbey Bourdon, Timo Keller, Zev Klagsbrun, David Lowry-Duda, Travis Morrison, Filip Najman, and Himanshu Shukla, and an appendix by Maarten Derickx and Mark van Hoeij), to appear in Mathematics of Computation.
  3. Self-dual matroids from canonical curves (with Alheydis Geiger, Bernd Sturmfels, and Raluca Vlad), to appear in Experimental Mathematics.
  4. Geometric quadratic Chabauty and p-adic heights (with Juanita Duque-Rosero and Pim Spelier), Special Issue in Honor of B. Edixhoven, Expositiones Mathematicae, 41, (2023), no. 3, 631–674.
  5. Quadratic Chabauty and p-adic Gross-Zagier, Transactions of the American Mathematical Society, 376, (2023), no. 5, 3725-3760.
  6. A geometric linear Chabauty comparison theorem (with Pim Spelier), Acta Arithmetica 202 (2022), no. 1, 67–88. 11G30 (11D45).
  7. 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.
  8. 38406501359372282063949 & all that: Monodromy of Fano Problems (with Borys Kadets), International Mathematics Research Notices (2020), rnaa275.
  9. Chabauty-Coleman computations on rank 1 Picard curves (with Travis Morrison), Arithmetic Geometry, Number Theory, and Computation, Simons Symposia, Springer, 2021, 485-506.
  10. 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.

I'm co-organizing a learning seminar on galois representations.

I'm co-organizing the algebra seminar at Brown University this year -- let me know your suggestions!

I organized "Number Theory meets Tropical Geometry: the semistable reduction of curves" at MPI Leipzig in April 17 - 21.

Teaching and Outreach