Glassy landscapes.
Activated dynamics.
The high-d landscapes paradigm: spin-glasses, and beyond (Review paper)
with Y. V. Fyodorov, Contribution to Spin Glass Theory and Far Beyond: RSB after 40 Years
Complexity of energy barriers in mean-field glassy systems
with G. Biroli and C. Cammarota
Distribution of rare saddles in the p-spin energy landscape
(Early Career Researcher Best Paper Prize 2022 of J.PhysA)
Curvature-driven pathways interpolating between stationary points:
the case of the pure spherical 3-spin model
with A. Pacco and G. Biroli
Dynamical Instantons and Activated Processes in Mean-Field Glass Models
with G. Biroli and C. Cammarota
High-d inference.
Ecology.
Random Matrices.
Complex energy landscapes in spiked-tensor and simple glassy models:
Ruggedness, arrangements of local minima, and phase transitions
with G.B. Arous, G. Biroli and C. Cammarota
Many problems in physics and computer science involve the minimization of complex high-dimensional functions encoding information (the signal) corrupted by randomness (the noise). The theoretical goal is to discriminate the regimes in which the signal is buried by the randomness and impossible to retrieve through minimisation, from those in which retrieval is possible but algorithmically challenging due to glassiness (proliferation of local minima where the optimisation algorithms get stuck). Understanding the landscape’s geometry — the distribution of local minima as a function of how informative they are — is key to understand the fate of optimization in high-dimension. In this work we introduce an analytical framework, the replicated Kac-Rice formalism, that allows us to characterize thoroughly the geometry of high-dimensional functions. We apply it to prototypical problems involving Gaussian landscapes, including the spiked-tensor problem in high-dimensional statistical inference.
Generalized Lotka-Volterra equations with random, non-reciprocal
interactions: the typical number of equilibria
with F. Roy, G. Biroli, G. Bunin and A. Turner
In recent years, there has been growing interest in analyzing complex ecosystems with multiple coexisting species (e.g., bacterial ecosystems). A central question is whether such ecosystems can have multiple equilibrium configurations and how these impact community dynamics. While existing techniques from mean-field theory of glasses address (at least partially) this question for models of ecosystems with random and symmetric interactions, assuming the reciprocity of the interactions is often not justified in the ecological context. In this work we use an analytical framework we have recently developed (the replicated Kac-Rice formalism) to characterize the multiple equilibria phase of species-rich ecosystems described by generalized Lotka-Volterra equations with non-reciprocal interactions. We count the numerous equilibrium configurations of the system and identify their properties (average abundance, diversity and dynamical stability), thus characterizing the dynamical attractors of the system dynamics.
Quantum localization &
integrability.
Local integrals of motion in many‐body localized systems (Review paper)
with J.Z. Imbrie and A. Scardicchio
Integrals of motion in the many-body localized phase
with M. Müller and A. Scardicchio
Remanent magnetization: signature of Many-Body Localization
in quantum antiferromagnets
with M. Mueller
Quantum
localization & glassiness
Fluctuation driven transitions in localized insulators:
Intermittent metallicity and path chaos precede delocalization
with M. Mueller, (editors' suggestion)
Anderson transition on the Bethe lattice: an approach with real energies
with G. Parisi, S. Pascazio, F. Pietracaprina and A. Scardicchio
Localized systems coupled to small baths: From Anderson to Zeno
with D.A. Huse, R. Nandkishore, F. Pietracaprina and A. Scardicchio
Forward approximation as a mean-field approximation for the Anderson and many-body localization transitions
with F. Pietracaprina and A. Scardicchio