My research focuses on moduli spaces and their geometry. This means that I am interested in constructing them, compactifying them and in computing some of their invariants (e.g. Chow groups, unramified cohomology, Brauer groups).

The kind of techniques that I use include stack-theoretical methods, logarithmic geometry, equivariant intersection theory and Galois cohomology. In my darkest times, I also use Mathematica or Sage for doing explicit computations (e.g. those that involve localization formulas).

## Research interests

- Moduli of curves, quasi-polarized K3 surfaces, Weierstrass fibrations, stable maps.
- Picard groups, integral Chow rings, equivariant intersection theory.
- Cohomological invariants (a.k.a. unramified cohomology) and Brauer groups.
- Quadratic intersection theory and Chow-Witt groups.
- Logarithmic geometry, compactification of Prym varieties.

## Preprints

- Wall-crossing integral Chow rings of $\overline{\mathcal{M}}_{1,n}$, joint with Luca Battistella (2024).
- The Brauer groups of moduli of genus three curves and plane curves, joint with Roberto Pirisi (2024).
- A criterion for smooth weighted blow-downs, joint with Veronica Arena, Giovanni Inchiostro, Siddharth Mathur, Stephen Obinna and Michele Pernice (2023).
- Degenerations of twisted maps to algebraic stacks, joint with Giovanni Inchiostro (2022).
- Polarized twisted conics and moduli of stable curves of genus two, joint with Angelo Vistoli (2021)
- Integral Picard group of some stacks of polarized K3 surfaces of low degree (2019).

## Publications

- Cohomological invariants and Brauer groups of algebraic stacks in positive characteristic, joint with Roberto Pirisi, to appear on Algebraic Geometry (2022).
- Effective morphisms and quotient stacks, joint with Giovanni Inchiostro, International Mathematics Research Notices, journal version (2023).
- Integral Picard group of moduli of polarized K3 surfaces, joint with Roberto Fringuelli and Angelo Vistoli, Bulletin of the LMS, journal version (2023).
- The integral Chow rings of moduli of Weierstrass fibrations, joint with Samir Canning and Giovanni Inchiostro, Transactions of the AMS, journal version (2022).
- Stable cuspidal curves and the integral Chow ring of $\overline{\mathscr{M}}_{2,1}$, joint with Michele Pernice and Angelo Vistoli, to appear on Geometry & Topology (2022).
- Intersection theory on moduli of smooth complete intersections, Mathematische Zeitschrift, journal version, (2022).
- Equivariant Chow-Witt groups and moduli stacks of elliptic curves, joint with Lorenzo Mantovani, Documenta Mathematica, journal version, (2021).
- Cohomological invariants of root stacks and admissible double coverings, joint with Roberto Pirisi, Canadian Journal of Mathematics, journal version, (2021).
- Brauer groups of moduli of hyperelliptic curves via cohomological invariants, joint with Roberto Pirisi, Forum of Mathematics, Sigma, journal version, (2021).
- A complete description of cohomological invariants of even genus hyperelliptic curves, joint with Roberto Pirisi, Documenta Mathematica, journal version, (2021).
- Integral Chow ring of the stack of smooth non-hyperelliptic curves of genus three, joint with Damiano Fulghesu and Angelo Vistoli, Transactions of the AMS, journal version, (2020).
- Picard group of moduli of curves of low genus in positive characteristic, Manuscripta Mathematica, journal version, (2020).
- Cohomological invariants of the stack of hyperelliptic curves of odd genus, Transformation Groups, journal version, (2020).
- The Chow ring of the stack of hyperelliptic curves of odd genus, International Mathematics Research Notices, journal version, (2019).
- On quantum and relativistic mechanical analogues in mean field spin models, joint with Adriano Barra, Francesco Guerra and Antonio Moro, Proc. R. Soc. A 470: 20140589 (2014).