Research

Research Interests

My research lies at the intersection of mathematical physics and probability theory, with a focus on quantum disordered systems, interacting fermionic systems, and constructive quantum field theory. I am particularly interested in the development and application of non-perturbative and unconventional methods to well-established problems.

Topics I have been working on include:

• Random Schrödinger operators, random band matrices, and supersymmetric nonlinear sigma models
• Many-body fermionic systems and their effective dynamics
• Stochastic quantisation and non-commutative stochastic analysis

Publications

• Exponential decay of correlations at high temperature in \(H^{2|2n}\) nonlinear sigma models.
  M. Disertori, J. Durán Fernández and L. Fresta
  Electron. J. Probab. 31, 1-27 (2026), arXiv:2603.26157.
• Spin transport and lack of quantisation for time-reversal symmetric insulators on the honeycomb structure.
  L. Fresta and G. Marcelli
  Ann. Henri Poincaré (2026), arXiv:2505.22452.
• Effective Dynamics of Local Observables for Extended Fermi Gases in the High-Density Regime.
  L. Fresta, M. Porta and B. Schlein
  Commun. Math. Phys. 406, 247 (2025)
• Non-commutative \(L^{p}\) spaces and Grassmann stochastic analysis.
  F. C. De Vecchi, L. Fresta, M. Gordina and M. Gubinelli
  Prob. Theor. Rel. Fields. 192, 949-1029 (2025)
• A stochastic analysis of subcritical Euclidean fermionic field theories.
  F. C. De Vecchi, L. Fresta and M. Gubinelli
  Ann. Probab. 53(3), 906-966 (2025)
• Effective Dynamics of Extended Fermi Gases in the High-Density Regime.
  L. Fresta M. Porta and B. Schlein
  Commun. Math. Phys. 401(3), 1701-1751 (2023)
• Approaching off-diagonal long-range order for 1+1-dimensional relativistic anyons.
  L. Fresta and P. Moosavi
  Phys. Rev. B 103, 085140 (2021)
• Supersymmetric Cluster Expansions and Applications to Random Schrödinger Operators.
  L. Fresta
  Math. Phys. Anal. Geom. 24, 4 (2021)
• A Supersymmetric Hierarchical Model for Weakly Disordered 3d Semimetals.
  G. Antinucci, L. Fresta and M. Porta
  Ann. Henri Poincaré 21, 3499-3574 (2020)
• Elementary test for nonclassicality based on the measurements of position and momentum.
  L. Fresta, J. Borregaard and A. S. Sørensen
  Phys. Rev. A 92, 062111 (2015)

Organisation and scientific activities

• Workshop From Randomness to Quantum Theory, Roma Tre University, 15 - 17 February 2027, together with Alessandro Giuliani
• Mathematical Physics Seminar, Roma Tre University (2026)
• Online seminar series Mathematical Challenges in Quantum Mechanics (2025–2026), together with Lucrezia Cossetti, Marco Falconi, Emanuela L. Giacomelli, Domenico Monaco and Marco Olivieri
• Hausdorff school "Recent developments in disordered systems", September 2024, Bonn, together with Johannes Alt and Michel Pain