## Douglas Ulmer Professor and Head |

## Recent research

I have been thinking about the Torelli locus $\mathcal{M}_g\hookrightarrow\mathcal{A}_g$ (the image of the moduli space of curves in the moduli space of principally polarized abelian varieties) and how it interacts with the Newton and Ekedahl-Oort stratifications of $\mathcal{A}_g$. In the first of three planned papers, Bryden Cais and I study unramified $\mathbb{Z}/p\mathbb{Z}$ covers of curves $Y\to X$ and look at how the $p$-torsion of the Jacobian of $Y$ is related to that of $X$. The preprint is available as arxiv:2307.16346.

## Students

I have projects for students at several levels. For the last few years, I have enjoyed working with advanced undergraduates on semester-length projects in number theory and related areas. I'd also be happy to talk with graduate students about projects in number theory and algebraic geometry ranging from a quick MS with good prospects for a paper to more substantial PhD projects.

## Contact

The fastest and most reliable way to reach me is via e-mail at `ulmer@math.arizona.edu`. To make an appointment, please contact my colleagues Alejandra (Ali) Gaona (520-621-2868, `agaona@math.arizona.edu`) or Aubrey Mouradian (520-621-2713, `aubreymouradian@math.arizona.edu`).

## Etc.

My short CV.

email: ulmer@math.arizona.edu | phone: 520-621-2868 | offices: Math 109 & ENR2 S311 |