Research

Academic research projects and publications spanning mathematical physics, quantum field theory, and topological data analysis.

Research

Research Fellowship — Multi-Domain Spectral Approach for the Computation of Fourier Transform

Sep 2021 — Jun 2022

Université Bourgogne Franche-Comté

Associate Researcher — Quantum Field Theory, Anomalies and Topological Phases

Jan 2020 — Jan 2021

Universidad de los Andes

Undergraduate Teaching Assistant — Physics & Mathematics

Sep 2016 — Dec 2019

Universidad de los Andes

Quantum Fields with Dynamical Boundary Conditions

Mar 2019 — Dec 2019

Universidad de los Andes

Studied aspects of Quantum Field Theory in flat and curved spacetimes in the context of the Casimir effect with subtle modifications on spacetime, observing that changes on vacuum introduce changes on observables of the physical system.

SPDC Characterization on Liquid Phase Exfoliated 2D Crystals for Piezoelectric Devices

Jan 2019 — Aug 2019

Universidad de los Andes

Characterized non-linear behavior of crystals, studying Spontaneous Parametric Down Conversion (SPDC) with the aim of obtaining a piezoelectric response on the material.

Compactificación de la métrica de Schwarzschild y estructuras causales

Aug 2018 — Dec 2018

Universidad de los Andes

Multi-disciplinary approach from Mathematics, Philosophy, and Computer Science to understand Schwarzschild metric compactification and its causality implications, complemented by computer simulations on the Einstein-Rosen black hole as an introduction to the Raychaudhuri equation and the Singularity Theorems.

Seminar on Quantum Field Theory and Mathematical Physics: Non-trivial Geometrical Effects on Flat Space-time

Aug 2018 — Nov 2018

Universidad de los Andes

Discussion of the quantum vacuum from the point of view of the Poincaré group of symmetries, studying phenomena such as the Casimir effect on a bidimensional cylinder, accelerated expansion space-time, and Rindler space-time using Quantum Field Theory on curved space-time.

Publications

  1. On numerical approaches to nonlinear Schrödinger and Korteweg–de Vries equations for piecewise smooth and slowly decaying initial data

    Klein, C., Prada-Malagón, J.D., & Stilov, N.

    Elsevier — Physica D — Nonlinear Phenomena · Nov 2023 · View

  2. Time-dependent topological analysis for cardiovascular disease diagnosis using magnetic resonance

    Prada-Malagón, J.D.

    CRAI Universitat de Barcelona — Dipòsit Digital UB · Sep 2023 · View

  3. Topological Phase Transitions and Non-commutative Geometry

    Prada, J.D. & Reyes, A.

    Research Project INV-2019-84-1833 — Ministerio de Ciencias · 2020

  4. Quantum Fields with Dynamical Boundary Conditions

    Prada Malagón, J.D.

    Universidad de los Andes · 2020 · View

  5. SPDC characterization on liquid phase exfoliated 2D crystals for piezoelectric devices

    Prada, J.D., Navarrete, C., Navarrete, C., Hernandez, Y., Valencia, A.

    Universidad de los Andes · 2019

  6. Compactificación de la métrica de Schwarzschild y estructuras causales

    Prada, J.D., Calderón, F., Laguna, M., Bargueño, P.

    Universidad de los Andes · 2018