news
| 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. |
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| 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. |
| Apr 03, 2024 | Some collaborators and I have solved an open case of the Inverse Galois Problem! We have realized the transitive group 17T7 as a Galois group over $\mathbb{Q}$. Here’s the polynomial we found: \(\begin{align*} x^{17} &- 2 x^{16} + 12 x^{15} - 28 x^{14} + 60 x^{13} - 160 x^{12} + 200 x^{11} - 500 x^{10} + 705 x^{9} - 886 x^{8}\\ &+ 2024 x^{7} - 604 x^{6} + 2146 x^{5} + 80 x^{4} - 1376 x^{3} - 496 x^{2} - 1013 x - 490 \, . \end{align*}\) |