About me

I am a Postdoc at SISSA, where I am part of the research group in Geometry and Mathematical Physics. My mentor is Andrea T. Ricolfi. I obtained the PhD degree in Geometry and Mathematical Physics at SISSA under the supervision of Ugo Bruzzo and Andrea T. Ricolfi.

Research

My research focuses on Algebraic Geometry, in particular, Resolution of singularities, classical Birational Geometry and Representation Theory are the areas I deal with the most. I am particularly interested in Hilbert schemes and, more generally, in the moduli spaces of coherent sheaves on algebraic varieties. I am also very interested in McKay correspondence, Minimal Model Program, positivity in Algebraic Geometry and Derived Categories.

To appear and published

The geometry of double nested Hilbert schemes of points on curves, with Paolo Lella, Sergej Monavari, Andrea T. Ricolfi and Alessio Sammartano.
Transactions of the American Mathematical Society 378, 6013-6047 (2025).
A counterexample to the parity conjecture, with Franco Giovenzana, Luca Giovenzana and Paolo Lella.
Algebraic Geometry, 12 (2025), no. 2, 173–188.
Unexpected but recurrent phenomena for Quot and Hilbert schemes of points, with Franco Giovenzana, Luca Giovenzana and Paolo Lella.
Rendiconti del Seminario Matematico - Politecnico di Torino, 82 (2024), no. 1, 145–170.
5d Conformal Matter, with Mario De Marco, Michele Del Zotto, Andrea Sangiovanni.
JHEP, Volume 2024, article number 306, (2024).
Moduli spaces of ℤ/kℤ-constellations over 𝔸².
Communications in Contemporary Mathematics, 27 (2025), no. 03, 2450019.
Growth and integrability of some birational maps in dimension three, with Giorgio Gubbiotti.
Annales Henri Poincaré, 13 July 2023.
On the Behrend function and the blowup of some fat points, with Andrea T. Ricolfi.
Advances in Mathematics, Volume 415 (2023), 108896.

Preprints

New components of Hilbert schemes of points and 2-step ideals, with Franco Giovenzana, Luca Giovenzana and Paolo Lella.
Invariants of nested Hilbert and Quot Schemes on surfaces, with Nadir Fasola, Danilo Lewański and Andrea T. Ricolfi.
Enumeration of partitions via socle reduction, with Sergej Monavari, Riccardo Moschetti and Andrea T. Ricolfi.
The Painlevé equivalence problem for a constrained 3D system, with Galina Filipuk, Giorgio Gubbiotti and Alexander Stokes
The motive of the Hilbert scheme of points in all dimensions, with Sergej Monavari, Riccardo Moschetti and Andrea T. Ricolfi.

Teaching

Complex algebraic surfaces - SISSA - Trieste - April-May 2025
schedule.
Computations in Algebraic Geometry - IMECC/UNICAMP - Campinas/SP - March 2025
Notes of the course, with Gessica Alecci.

Events organisation

TULSF IX
A meeting in Algebraic Geometry
SISSA, Trieste, 7 November 2024.
Co-organised with U. Bruzzo, E. Pavia.
WAGP24 ALGEBRO-GEOMETRIC TECHNIQUES FOR PHYSICS: BUNDLES, STACKS AND SUPERGEOMETRY
A celebration of Daniel Hernández Ruipérez’s 70th Birthday
IGAP, Trieste, 3-7 June 2024.
Co-organised with U. Bruzzo, B. Graña Otero, D. Hernandez Serrano, D. Sánchez Gómez.
The Geometry of Hilbert Schemes of Points
CIRM, Levico Terme, 6-10 May 2024.
Co-organised with Paolo Lella, Sergej Monavari, Andrea T. Ricolfi and Alessio Sammartano.

Motives Calculator

At this link you can find a motives calculator based on the results obtained in the paper "The motive of the Hilbert scheme of points in all dimensions" in collaboration with with Sergej Monavari, Riccardo Moschetti and Andrea T. Ricolfi.

It's Better To Visualize It ( ) is a software made in by me. It allows to visualize plane partitions and to edit them via simple clicks. Here you find a sample online version. You also find a version, a version and an version. IBTVI is also available on Google Play

Interests and hobbies

Music, politics and chess.

Michele Graffeo

Institutional webpage - CV
PhD thesis