Sam Schiavone

I am a Ph.D. mathematician, researcher, and programmer who combines mathematical abstraction with computational tools in order to discover, analyze, and elucidate. My expertise lies in translating theoretical concepts into practical solutions.

Previously I was a research scientist in the mathematics department at MIT, supervised by Bjorn Poonen and Drew Sutherland, as part of the Simons Collaboration on Arithmetic Geometry, Number Theory, and Computation. I received my Ph.D. in mathematics from Dartmouth College in 2019 under the supervision of John Voight.

news

Nov 20, 2025	I participated in the Erdős Institute’s Data Science Boot Camp. In addition to attending video lectures and completing exercises on the theory and practice of data science, I worked on a group project on developmental linguistics and language acquisition. We used developmental data from Stanford’s Wordbank dataset to engineer new features, added them to a dataset derived from the results of Duolingo users, and measured how much they improved predictions of second-language learning. You can find our article, slides, and a video of our presentation here, and our code here.
Sep 30, 2025	Our preprint Mumford-type Shimura curves contained in the Torelli locus is now on arXiv. We present two Shimura curves of Mumford type contained in the Torelli locus, one whose universal family is a hyperelliptic curve, and the other non-hyperelliptic, both of genus 4. The Jacobians of these curves are the first explicit examples of abelian varieties of the type described by Mumford in his article A Note of Shimura’s paper “Discontinuous Groups and Abelian Varieties”. You can find related code in our GitHub repo. In particular, the file Shimura_models.m contains equations for the universal curves of genus 4 mentioned above.
Jun 12, 2025	I am speaking at LuCaNT 2025 in Providence on July 9th. I will talk about a new section of the LMFDB on finite groups that I helped develop. For details, see our preprint, which will be published in the conference proceedings. Pitchayut “Mark” Saengrungkongka, an MIT undergrad, is also speaking at LuCaNT. I mentored Mark and Noah Walsh last summer as they worked on a research project on gluing curves along their torsion, a project based on my article with Jeroen Hanselman and Jeroen Sijsling. Congrats to Mark and Noah on a very successful project! You can find their preprint here.
Feb 03, 2025	Some collaborators and I have discovered explicit equations for 2 families of abelian 4-folds of Mumford type. Explicit examples have been sought after for many years; see this blog post by Frank Calegari for more details. Stay tuned for our preprint!
Nov 12, 2024	Our preprint 17T7 is a Galois group over the rationals is now on arXiv. The new polynomial has also been added to the LMFDB and the Klüners–Malle database.

selected publications

Mumford-type Shimura curves contained in the Torelli locus

Thomas Bouchet, Jeroen Hanselman, Andreas Pieper, and 1 more author

Preprint, arXiv:2510.00093 [math.AG], 2025

Abs arXiv

In this article we give explicit equations for two Shimura families of genus 4 curves whose Jacobians are abelian fourfolds of Mumford type. These are the first explicit examples of abelian varieties over QQ with endomorphism algebra ZZ and additional Hodge tensors.
17T7 is a Galois group over the rationals

Raymond Bommel, Edgar Costa, Noam D. Elkies, and 3 more authors

Preprint, arXiv:2411.07857 [math.NT], 2024

Abs arXiv

We prove that the transitive permutation group \textsf17T7, isomorphic to a split extension of C_2 by \PSL_2(\F_16), is a Galois group over the rationals. The group arises from the field of definition of the 2-torsion on an abelian fourfold with real multiplication defined over a real quadratic field. We find such fourfolds using Hilbert modular forms. Finally, building upon work of Dembélé, we show how to conjecturally reconstruct a period matrix for an abelian variety attached to a Hilbert modular form; we then use this to exhibit an explicit degree 17 polynomial with Galois group \textsf17T7.
Equations of genus 4 curves from their theta constants

Jeroen Hanselman, Andreas Pieper, and Sam Schiavone

Preprint, arXiv:2402.03160 [math.AG], 2024

Abs arXiv

In this article we give explicit formulas for the equations of a generic genus 4 curve in terms of its theta constants. The method uses the Prym construction and the beautiful classical geometry around it.