Pablo Miranda Rozas
🎓 Associate Professor · USACH

Pablo
Miranda Rozas

Department of Mathematics and Computer Science,
Universidad de Santiago de Chile.

Mathematical Physics Spectral Theory Magnetic Schrödinger Operators Quantum Resonances Discrete Operators
📨 Contact 📄 CV 📚 Publications
Photo of Pablo Miranda Rozas

About

Bio

I am an Associate Professor at the Department of Mathematics and Computer Science (DMCC) of the Universidad de Santiago de Chile (USACH). My research lies at the interface of mathematical physics and spectral theory, with a particular focus on magnetic Schrödinger operators, quantum resonances, and spectral properties of discrete operators. I currently serve as Head of the MSc Program at DMCC.

15+
Publications
3
FONDECYT grants (PI)
10+
Years teaching
3
Graduate students

Research

Research lines

Magnetic Schrödinger operators
Distribution of eigenvalues and spectral shift function asymptotics.
Quantum waveguides
Resonances in deformed quantum waveguides.
Discrete operators
Spectral properties of discrete Schrödinger and Dirac operators on lattices.

Funding

Selected projects

  • FONDECYT Regular 1241983 PI · Active
    Spectral properties of continuous and discrete quantum Hamiltonians
    2024 – 2027
  • Visiting Scholar — Université de Bordeaux
    Physique-Mathématique Bordeaux–Santiago program
    February – June 2024
  • FONDECYT Regular 1201857 PI · Completed
    Resonances and spectral shift function for magnetic systems
    2020 – 2023

Research output

Selected publications

  • 2025
    Spectrum of the perturbed Landau-Dirac operator
    Bruneau, V.; Miranda, P.
    Annales Henri Poincaré DOI ↗
  • 2025
    Clusters of resonances for a non-selfadjoint multichannel discrete Schrödinger operator
    Assal, M.; Bourget, O.; Miranda, P.;Sambou, D.
    Journal of Mathematical Physics 66, 073504
  • 2025
    Eigenvalue Asymptotics Near a Flat Band in the Presence of a Slowly Decaying Potential
    Miranda, P..;Parra, D.
    Asymptotic Analysis 142(4)
  • 2025
    Semiclassical resolvent estimates for matrix Schrödinger operators and applications
    Assal, M.; Miranda, P.;Zerzeri, M.;
    Reviews in Mathematical Physics 37(05), 2450043
  • 2025
    Singularities of the magnetic spectral shift function for potentials of variable sign
    Bruneau, V.;Miranda, P.; Levitina, G.
    Journal of Spectral Theory DOI ↗
  • 2023
    Continuum Limit for a Discrete Hodge-Dirac Operator on Square Lattices
    Miranda, P.; Parra, D.
    Letters in Mathematical Physics 113, 45
  • 2023
    Spectral Asymptotics at Thresholds for a Dirac-type Operator on ℤ²
    Miranda, P.; Parra, D.; Raikov, G.;
    Journal of Functional Analysis 284(2)

Teaching

Courses

  • Introduction to PDEsUndergraduate USACH · 2026
  • Topology and Geometry IGraduate USACH · 2020 & 2023
  • Spectral TheoryGraduate USACH · 2021 & 2023
  • Analysis IGraduate USACH · 2018–2019
  • Differential GeometryUndergraduate USACH · 2022
  • Measure Theory / Functional AnalysisUndergraduate USACH · 2018–2025
  • Calculus I, II & III Undergraduate UTFSM & PUC · 2014–2017

Roles

Administration

  • Head of the MSc Program
    Department of Mathematics, USACH · 2022–present
  • Deputy Director of Research
    Department of Mathematics, USACH · 2022–2024
  • Coordinator of the course Calculus 2.
    School of Engineering, USACH · 2019–2022

Contact

Get in touch

✉️
Email pablo.miranda.r@usach.cl
🏛️
Affiliation Departamento de Matemática y Ciencia de la Computación, Universidad de Santiago de Chile
📍
Address Las Sophoras 173, Estación Central, Santiago, Chile

Profiles

Online profiles

📘 Google Scholar ↗ 🟢 ORCID ↗ 📄 Curriculum Vitae ↗