CV
Here is my CV (last update 01/2026)
Contact Information
| Name | Guido Mazzuca |
| Professional Title | Mathematics Professor |
| gmazzuca@tulane.edu | |
| Location | 6823 St Charles Ave, New Orleans, Louisiana LA 70118 |
Professional Summary
I am a mathematician driven by the philosophy that mathematics should be seen, not just written. While my research tackles the rigorous intersection of Integrable Systems and Random Matrix Theory, my passion extends equally to education and community outreach. From visualizing complex concepts on my YouTube channel MathyOwl to organizing student programs like BATS and GIST, I am dedicated to bridging the gap between advanced research and accessible education.
Experience
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2023 - present New Orleans, LA
Postdoctoral Researcher
Tulane University
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2021 - 2023 Stockholm, Sweden
Postdoctoral Researcher
KTH Royal Institute of Technology , Stockholm, Sweden
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2023 - present New Orleans, LA
Organizer
BATS and GIST
Organizer for BATS and GIST math outreach programs.
Education
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2017 - 2021 Trieste, Italy
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2012 - 2017 Milan, Italy
Bachelor and Master's Degree
University of Milan
Mathematics
Publications
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2023 Adiabatic invariants for the FPUT and Toda chain in the thermodynamic limit.
Communications in Mathematical Physics
We study the periodic Fermi-Pasta-Ulam-Tsingou system as a perturbation of the periodic Toda lattice equations. Exploiting this idea, we show that the Toda integral of motions are adiabatic invariants for the Fermi-Pasta-Ulam-Tsingou system in the thermodynamic limit. This result holds in probability with respect to the Gibbs measure of the system.
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2024 Generalized Gibbs ensemble of the Ablowitz-Ladik lattice, circular beta-ensemble and double confluent Heun equation
Annales Henri Poincaré
In this paper, we prove a polynomial Central Limit Theorem for several integrable models, and for the β ensembles at high-temperature with polynomial potential. Furthermore, we are able to relate the mean values, the variances and the correlations of the moments of these integrable systems with one of the β ensembles. Moreover, we show that for several integrable models, the local functions’ space-correlations decay exponentially fast.
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2023 Generalized Gibbs ensemble of the Ablowitz-Ladik lattice, circular beta-ensemble and double confluent Heun equation
Communications in Mathematical Physics
We consider the discrete defocusing nonlinear Schrödinger equation in its integrable version, which is called defocusing Ablowitz-Ladik lattice. We consider initial data sample according to the Generalized Gibbs ensemble for this lattice with periodic boundary conditions with period N. In this setting, the Lax matrix of the Ablowitz-Ladik lattice is a random CMV-periodic matrix, and it is related to the Killip-Nenciu circular β-ensemble at high-temperature. Furthermore, we obtain the generalized free energy of the Ablowitz-Ladik lattice and the density of states of the random Lax matrix by establishing a mapping to the one-dimensional log-gas. For the Gibbs measure related to the Hamiltonian of the Ablowitz-Ladik flow, we obtain the density of states via a particular solution of the double-confluent Heun equation.
Skills
Languages
Interests
Projects
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Mathematical Fundation of Soliton Gas theory and Generalized Hydrodynamics
Study of the mathematical aspects of Soliton Gas theory and Generalized Hydrodynamics (GHD) for integrable PDEs.
- Soliton Gas
- Generalized Hydrodynamics
References
- Professor Tamara Grava
PhD Advisor. SISSA - Scuola Internazionale Superiore di Studi Avanzati.
- Professor Alberto Maspero
PhD Advisor. SISSA - Scuola Internazionale Superiore di Studi Avanzati.
- Professor Ken McLaughlin
Postdoctoral Mentor. Tulane University.
- Professor Herbert Spohn
Collaborator.