Jessica Trespalacios Julio

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Currently, I am Fondecyt ANID postdoctoral researcher, with the project: Unsolved Integrability Mysteries: from Kadomtsev-Petviashvili solitons to Einstein's Black Holes, at the Institute of Physical and Mathematical Sciences at Universidad Austral de Chile, under the supervision of Prof. Felipe Poblete.

Prior, I completed my Ph.D. Thesis at Department of Mathematical Engineering (DIM) of the University of Chile, under the advice of Prof. Claudio Muñoz and Prof. Miguel Á. Alejo. Previously, I obtained my M.Sc. in Applied Mathematics at the University of Puerto Rico, at Mayaguez, and my B.Sc. in Mathematics at the University of Cartagena.

Contact information: jtrespalacios@dim.uchile.cl, jessica.trespalacios@uach.cl

CV Here

Research

Academic Service

Mathematical General Relativity

Prisma: Mujeres Matemáticas

Upcoming Events

First PRISMALab Meeting (Registration)

My research interest

I am interested in Nonlinear Analysis, Dispersive Partial Differential Equations and its relation to Mathematical General Relativity , in specific:

Mathematical study of Einstein field equations in vacuum, cosmological-type solution, their stability.
Conservations laws, and global existence theory.
Virial method for the study of asymptotic behavior of the gravitational wave type solitonic solutions.
Dispersive equations, in particular, hyperbolic models and the blow-up dynamics

Curriculum

Graduate Faculty Accreditation, Austral University of Chile, 2026–2031. Accredited by the Office of Graduate Studies to teach Master’s-level courses, supervise Master’s theses, and serve as instructor for 300-level graduate courses.
Summer Postdoctoral Program 2026, Instituto de Matemática Pura e Aplicada (IMPA). Supervised by Prof. Felipe Linares. Competitive grant. Jan.-Feb 2026
Postdoctoral Researcher. Center of Mathematical Modeling (CMM)–University of Chile. December 2024- April 2025.
Award for best PhD thesis in Exact Sciences 2025. Chilean Academy of Sciences.
FONDECYT National Postdoctoral Project. ANID 2025. Austral University of Chile. Ranked first in the mathematics area.
Graduate Distinctions 2024: Prize of best Ph.D. thesis, Graduate School of the Faculty of Physical and Mathematical Sciences, University of Chile.
Graduate Distinctions 2024: Prize for the best Ph.D. student, Graduate School of the Faculty of Physical and Mathematical Sciences, University of Chile.
Ph.D. graduated with high distinction, DIM, University of Chile, 2024. Thesis: Soliton Dynamic in Einstein Field Equation.
ANID Doctoral internship, 2022. Georgia Tech University.
ANID Complementary Funds (travel and study materials), 2022.
ANID National PhD Fellowship, 2019-2024. University of Chile
Magister in Applied Mathematics. UPRM, 2014. Thesis: Explicit solutions for non-autonomous diffusion reaction equations using Ermakov and Riccati systems
Fellowship: Tuition and stipend exemption granted by the UPRM, 2012-2014.
Scholarship: Tuition exemption for the best semester average (9 semesters), University of Cartagena, 2006-2011.
Bachelor in Mathematics at the University of Cartagena. First-class honors, University of Cartagena, 2011.

Conferences and workshops 2026

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