Interview with Emanuele Macrì, invited speaker at ICM2022

Link to the virtual ICM 2022 talks

What is your field of research?

I work in algebraic geometry, by using modern techniques of wall-crossing and stability conditions in derived categories as a tool to answer questions with a more classical flavour.

Vector bundles on algebraic varieties, stability conditions, moduli spaces, and variation of stability, i.e., ‘wall-crossing’, have been used in algebraic geometry since many years, with outstanding results. The notion of stability in the derived category is more recent: it arose from the physics literature and it was formalized by Bridgeland in the beginning of 2000’s. The idea is to mimick the classical approach with vector bundles, but with the flexibility that the derived category allows.

Are there place or encounters that were decisive in your career? Or findings that had a profound effect on the way you do mathematics?

My work benefited immensely from the input of my mentors, collaborators and friends.

Arend Bayer, with whom we share the talk at the ICM, and Paolo Stellari have been of utmost importance for me.

I have fond memories of my postdoctoral years shared with them, either in the stimulating atmosphere in Bonn, under the direction and influence by Daniel Huybrechts, or at the University of Utah, where Aaron Bertram envisioned many of the ideas which we worked on in the following years and persistently encouraged us to explore them.

What do you like about being a mathematician?

I like very much the freedom of choosing a problem to work on, by taking the time to think properly about it, without rushing through it. Coming back to the problem years after, make maybe some little progress, get stuck again, and continue.

I also like very much the learning and mentoring part, both regarding teaching and supervising PhD students and postdocs. I learned from Herb Clemens, during my years at the Ohio State University, to run a morning seminar in a relaxed and inclusive atmosphere where, while trying to understand new topics through examples, we get stuck at the blackboard while attempting to solve them, just to find a solution together. I am missing in the last years, due to the recent pandemic, the feeling of those meetings, but I plan to start again this soon!

Have you already decided what you will talk about at the ICM ?

The format of the talk changed quite a bit.

Arend and I will pre-record an online talk, in the slightly non-standard format of a Zoom discussion and then present an actual in person talk at the ICM event at ETH in Zurich a few days after.

We decided to speak about the recent developments of Bridgeland stability conditions in the context of Kuznetsov components.

This has a strong classical flavour, in the theory of Fano manifolds, but with the modern viewpoint of derived categories and semiorthogonal decompositions.