PhD

My research focuses on exploring potential connections between moduli spaces and stacks in algebraic geometry, and the theory of Lie algebras and quantization in representation theory.

Prospective students are encouraged to visit my publications page for an overview of my current research directions.

Possible PhD thesis topics include:

  • Cohomological Hall algebras of singular curves or surfaces,
  • Families of cohomological Hall algebras,
  • Cohomological Hall algebras and Bridgeland’s stability conditions.

Feel free to drop me an email in case they would like to know more.

As stimulating guidelines for potential Ph.D. students, I suggest reading Daniel Halpern-Leistner’s advising philosophy and Ravi Vakil’s page for potential PhD students. The potential reader should be aware that a PhD fellowship in the USA usually lasts 5 years, hence some of the ideas suggested in loc. cit. cannot work in the Italian system. On the other hand, some advice is independent of the institution and the duration of the fellowship, such as:

  • Mathematics is not just about answering questions; even more so, it is about asking the right questions, and that skill is a difficult one to master.

  • Think actively about the creative process. In an undergraduate class, the students have tried to learn absolutely all the material flawlessly. But to know everything needed to tackle an important problem on the frontier of human knowledge, one would have to spend years reading many books and articles. So they will have to learn differently. But how?

  • When learning a new theory, try to calculate some toy cases, and think of some explicit basic examples.

  • Talk to other graduate students (and organize reading groups with them), post-docs, faculty, visitors, etc.

  • Weekly meetings are beneficial. A student could prefer not to meet in a given week if they have nothing much to report, but those weeks are particularly important to meet.

  • A main achievement of supervising is helping PhD students become excellent researchers. This could be obtained by providing ambitious but achievable PhD projects, giving constructive feedback, nurturing a supportive, safe, and fun research environment, and supporting their professional development.

  • A supervisor may expect that PhD students work hard (e.g. work through challenges; produce deliverables on time, follow through on commitments they make; etc.) and take initiative (e.g. own your research, identify what the next steps could be, and take it there!), provide progress upgrades (about what has been done, what went well and what challenges arose, and what new questions were posed), and keep track of their work plan.