About Me

I am a PhD Candidate in Mathematics in the joint doctoral program between UTFSM, UV, and PUCV. My research focuses on control theory, inverse problems, and stochastic partial differential equations (SPDEs).

Publications & Preprints

Journal Articles

  • Lecaros, R., Pérez, A. A., & Prado, M. F. Inverse Random Source and Cauchy Problems for Semi-Discrete Stochastic Parabolic Equations in Arbitrary Dimensions.
    Inverse Problems (2026). [Journal] [arXiv]
  • Lecaros, R., Pérez, A. A., & Prado, M. F. Carleman estimate for semi-discrete stochastic parabolic operators in arbitrary dimension and applications to controllability.
    Applied Mathematics and Optimization (2025). [Journal] [arXiv]

Preprints

  • Lecaros, R., Pérez, A. A., & Prado, M. F. Controllability for semi-discrete semilinear stochastic parabolic operators.
    Submitted on Apr 6, 2026. [arXiv]

Grants, Projects, Research Stays & Fellowships

Research Stays & Visits

  • Visiting Researcher, Department of Mathematics, Sichuan University, Chengdu, China (2026).
    Collaborator: Prof. Qi Lü. Focus on stochastic control theory and SPDEs.

Grants & Funded Projects

  • Programa de Incentivo a la Iniciación Científica (PIIC) Grant N° 020/2026 — Dirección de Postgrado, UTFSM (2026).
    Project: "Controlabilidad nula para ecuaciones parabólicas estocásticas semidiscretas con condiciones de borde dinámicas."
    Advisor: Prof. Rodrigo Lecaros.
  • PIIC Grant N° 049/2025 — Dirección de Postgrado, UTFSM (2025 – 2026).
    Project: "Estimaciones de Carleman y null-controllability en ecuaciones diferenciales parabólicas estocásticas semilineales en el marco semidiscreto multidimensional."
    Advisor: Prof. Rodrigo Lecaros.
  • DGI Research Project PI_LIR_25_14 — Dirección de Investigación, UTFSM.
    Project: "Controlabilidad y problemas inversos de ecuaciones de ondas en transmisión."
    Principal Investigator: Prof. Alberto Mercado Saucedo. Co-Investigator: Prof. Rodrigo Lecaros Lira. Role: Doctoral Student Researcher.
  • FIB-UV Doctoral Scholarship (Fondo Institucional de Becas), Universidad de Valparaíso.
    Full tuition and maintenance doctoral scholarship.

Teaching Experience

Lecturer / Adjunct Professor (Profesor Part-Time)

Departamento de Matemática, Universidad Técnica Federico Santa María (Campus San Joaquín)

  • MAT-060: Algebra and Geometry — 2025/1, 2026/1
  • MAT-070T: Introduction to Calculus workshop — 2025/2, 2026/1
  • MAT-022: Mathematics II (Multivariable Calculus & Linear Algebra) — 2024/2, 2025/1, 2025/2

Graduate Teaching Assistant

Joint PhD & Master's Program in Mathematics, UTFSM

  • Control Theory and Inverse Problems (Graduate Level) — 2 Semesters

Undergraduate Teaching Assistantships

Universidad del Valle (Univalle) & UTFSM

  • Calculus, Linear Algebra, and Analysis Courses — Multiple terms.

Talks & Academic Events

Talks & Presentations

  • Inverse problems for the semidiscrete stochastic parabolic equations (poster).
    IPPhys Summer School, Puerto Varas, Chile (2026).
  • Inverse problem for semidiscrete stochastic parabolic operators in arbitrary dimensions.
    XCIII Encuentro Anual de la Sociedad de Matemática de Chile (SOMACHI), Vicuña, Chile (2025).
  • Carleman estimates for semi-discrete stochastic parabolic operator and application to controllability.
    2nd Colombian Workshop in Nonlinear Dispersive Equations, Santiago de Cali, Colombia (2025).
  • Las estimaciones de Carleman en el contexto estocástico y semidiscreto.
    Seminario especial de egresados y estudiantes de matemáticas (CONVImaTE), Santiago de Cali, Colombia (2025).
  • Carleman estimates for semi-discrete stochastic parabolic operator and application to controllability.
    XCII Encuentro Anual de la Sociedad de Matemática de Chile (SOMACHI), Valdivia, Chile (2024).
  • Unique continuation and approximated controllability associated with a linearization of the ab-Boussinesq system with space-dependent potentials.
    XCI Encuentro Anual de la Sociedad de Matemática de Chile (SOMACHI), Santiago, Chile (2023).

Attended Conferences & Workshops

  • Summer School EUR MINIT — Control, inverse problems and spectral theory, Institut de Mathématiques de Toulouse, University of Toulouse, France (2025).
  • Conferences: Control of PDEs and related topics, Institut de Mathématiques de Toulouse, University of Toulouse, France (2025).
  • I Escuela de Postgrado en Matemática, Universidad de la Frontera, Temuco, Chile (2024).
  • VI Summer School in Probabilities and Stochastic Processes, Center for Mathematical Modeling (CMM), Universidad de Chile, Chile (2024).

Academic Service

Seminar Organization

  • Co-founder, Seminario: Topología del Cerrito.
    Universidad Técnica Federico Santa María (2026 – Present).

Journal Peer Reviewing

Referee for international indexed journals (Web of Science):

  • Inverse Problems (IOP Publishing) — 2 reviews