Kevin D. Silva Pérez
Personal Academic Website

Kevin David Silva Pérez

PhD Student in Computational Mathematics and Statistics

I work on partial differential equations, nonlocal operators, analysis on irregular domains, diffusion processes, and heat flow in complex geometries, with growing interest in probabilistic methods and PDE-informed machine learning.

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Affiliation University of Puerto Rico – Río Piedras
Advisor Alejandro Vélez-Santiago
Research Focus PDEs, fractals, nonlocal analysis
Languages Spanish, English
Portrait of Kevin David Silva Pérez
Mathematics, probability, nonlocal analysis, and scientific computing.

About

I am currently pursuing a PhD in Computational Mathematics and Statistics at the University of Puerto Rico, Río Piedras. My work lies at the intersection of analysis, geometry, and applied mathematics, with emphasis on partial differential equations over non-smooth and irregular domains.

I am especially interested in fractional Laplacian operators, anomalous diffusion, heat kernels, ramified and fractal structures, and the emerging interface between PDE theory and machine learning methods such as PINNs and operator learning.

  • Partial differential equations and boundary value problems
  • Fractional Laplacian and nonlocal operators
  • Analysis on fractals and ramified domains
  • Diffusion processes and heat flow in complex geometries
  • Functional and classical analysis
  • PDEs and machine learning / operator learning

Current Research

Fractional Laplacian operators on non-smooth and irregular sets

In progress
Study of nonlocal operators on irregular geometries with applications to anomalous diffusion, boundary effects, and fine regularity theory.

PDE-informed machine learning

In progress
Exploration of DeepONets, PINNs, and related methods for scientific computing, operator approximation, and PDE-constrained learning problems.

Funded project: FIPI 2024–2026

University of Puerto Rico – Río Piedras
Award Number: 20FIPI570025
New trends in regularity theory for boundary value problems over non-smooth domains. Role: theoretical analysis of boundary value problems on irregular domains and regularity methods.

Previous funded research project

Puerto Rico Science, Technology & Research Trust
Agreement 2022-00014
Boundary value problems of nonstandard growth structure over real-world regions. Role: mathematical modeling and analysis of PDEs with nonstandard growth.

Education

PhD in Computational Mathematics and Statistics

University of Puerto Rico – Río Piedras
2023 – Present

MSc in Applied Mathematics

University of Puerto Rico – Mayagüez
2021 – 2023
Thesis: Diffusion over Domains with Ramified Fractal Boundaries

Bachelor in Mathematics

Universidad de Cartagena, Colombia
2017 – 2020
Advisor: Alejandro Vélez-Santiago, PhD

Publications

Diffusion over ramified domains: solvability and fine regularity
Silva-Pérez, K.; Vélez-Santiago, A.
Calculus of Variations and Partial Differential Equations 64 (2025), Article no. 238
PDE Fractals Regularity Theory
Calculus with MATLAB
Silva-Pérez, K.; Arrieta-Montalvo, R.; Ortega, P.; Johnson, B.
Editorial Universidad de Cartagena, 2021
Book MATLAB Calculus Education

Selected Talks and Conferences

Great Plains Operator Theory Symposium (GPOTS 2025)

University of Puerto Rico – Río Piedras
October 20–24, 2025
Talk: Elliptic Problem over Ramified Domains.

Workshop in Partial Differential Equations: Theory and Applications

University of Puerto Rico – Mayagüez
October 7–10, 2025
Poster: Diffusion over Bronchial Trees: Construction and Approximation Results.

LatMath 2025

IPAM, UCLA, Los Angeles, CA
March 7–11, 2025
Poster: Diffusion on Bronchial Trees: Construction and Approximation Results.

Analysis on Fractals and Networks, and Applications

CIRM, France
March 18–22, 2024
Poster: Diffusion on Bronchial Trees: Construction and Approximation Results.

13th AIMS Conference on Dynamical Systems, Differential Equations and Applications

Wilmington, NC
May 31 – June 4, 2023
Talk: Diffusion over Bronchial Trees: Fine Regularity (with A. Vélez-Santiago).

Teaching and Academic Roles

Teaching Experience

  • Calculus I–III
  • Precalculus I–II
  • Mathematical Appreciation
  • Differential Equations
  • College Board and SAT instruction

Academic Positions

  • Researcher, UPR Río Piedras (2025–Present)
  • Teaching Assistant, UPR Río Piedras (2023–2025)
  • Research Assistant, UPR Mayagüez (2022–2023)
  • Teaching Assistant / Instructor, UPR Mayagüez (2021–2022)
  • Tutor, Universidad de Cartagena (2019–2021)

Service, Leadership, and Skills

Service and Memberships

  • Reviewer, Colciencias (Colombia), 2022–2024
  • Member, SACNAS
  • Member, Asociación Estudiantil de Matemáticas, UPRRP
  • Volunteer, American Red Cross, Puerto Rico
  • Member, Fractals and PDEs Research Group

Leadership

Founder and Academic Advisor of TURI (Teoría, Universo, Razonamiento e Investigación), an interdisciplinary academic initiative focused on mathematics, AI, physics, research workshops, and scientific communication.

Skills

  • Python
  • MATLAB
  • R
  • LaTeX

Teaching Interests

  • Calculus and multivariable calculus
  • Differential equations
  • Linear algebra
  • Real and functional analysis
  • Probability and statistics
  • PDEs and mathematical modeling

Contact

Email: kevin.silva1@upr.edu

Phone: +1 (787) 487-7696

Location: San Juan, Puerto Rico

Profiles: ResearchGate · GitHub

A polished public version can later include Google Scholar, ORCID, MathSciNet links, downloadable papers, and a dedicated research statement.