# Research interests

My research interests mainly focus on statistical field theory and critical phenomena, rough energy landscapes, spin-glass models and interdisciplinary applications.

My work so far has dealt with a variety of topics:

Renormalization Group techniques and critical phenomena;

Problems at the crossroad between the physics of glasses and the mathematics of constrained satisfiability;

Mean-field models for amorphous solids under shear deformations;

Development of dynamical mean-field theory formalism to investigate out-of-equilibrium dynamics and aging;

In-depth analysis of theoretical ecology models.

Spin glasses and perturbative RG

My expertise is mainly related to infinite-dimensional models. Nevertheless, to cover a broader spectrum of phenomena and extend predictions beyond mean field, I have also worked out perturbative renormalization group techniques in Edwards-Anderson models and Bethe lattices.

The theoretical framework proposed in Ref [4], valid both in the ordered and disordered phase, focuses on the definition of a Bethe multi-layer construction. It allows us to write a perturbative series in terms of fat diagrams and to compute finite-size corrections near the critical point.

In 2022 in collaboration with M. Baity-Jesi, I wrote the review "Introduction to the Theory of Spin Glasses", to appear in 2023 in the 2nd edition of "Encyclopaedia of Cond. Matt. Physics" by Elsevier [14].

Constraint satisfaction problems

One topical aspect of my doctoral research concerned the exact derivation of an effective free energy functional (Thouless-Anderson-Palmer free energy) to investigate critical properties of the spherical perceptron in the non-convex phase.

Such a formalism has been also generalized to high-dimensional sphere models near jamming (a.k.a. a rigidity transition taking place inside the glassy phase at zero temperature).

Jamming and Yielding transitions

The response of amorphous solids to an applied shear deformation is a timely problem, both in fundamental and applied research. To address challenging questions in this field, I focused on systems of hard spheres (and variants modelled by a square-well potential with a small attractive part) in infinite dimensions taken as a reference model for colloidal systems and granular matter. This approach allowed us to perform a systematic exploration of the phase diagram.

Models and Applications in Ecology & Evolution

I am also interested in investigating emergent phenomena and critical, collective dynamics in large interacting ecosystems through methods and concepts rooted in statistical physics.

During the last (almost) five years, I have extensively been working on two benchmarks in theoretical ecology:

i) a reformulation of MacArthur's model;

ii) the random Lotka-Volterra model, both with competitive and intra-specific cooperative interactions.

More details can be found in Refs. [7], [10], [11] ,[12].

In 2022, I also wrote a short review on disordered system methods applied to ecology as a Special Issue of "Spin Glass Theory and Far Beyond - 40 Years later".

See Ref. [13].