Darren Schmidt received his PhD in 2026 with a thesis titled Ekedahl-Oort Types and Newton Polygons of Special Families of Curves.
Eros Sunny is expected to receive a PhD in 2027.
My research focus is arithmetic geometry, which is at the boundary of number theory and algebraic geometry. To conduct research in this area, you need background in algebraic number theory and algebraic geometry, both of which rely on graduate-level algebra. If you were an ambitious student at a top-tier math department, you could have started learning about these as an undergraduate, but more realistically this will happen in the first few years of graduate school. This needs to happen fast so you can learn about a more specialized topic and begin conducting research. At the same time, you also want to obtain a broad background in many areas of mathematics.
David Zureick-Brown has some advice for graduate students in arithmetic geometry which is good for someone interested in an academic career. If you're not interested in being a researcher in the field, you can get away with less background with the support of your advisor (at the expense of being less independent).