Jessica P. Trespalacios Julio
Welcome to my homepage
I am a fourth year PhD student at Department of Mathematical Engineering (DIM) of the University of Chile, under the advise of Prof. Claudio Muñoz. 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 - jtrespalacios@ug.uchile.cl
My research interest
I am interested in Nonlinear Analysis, Partial Differential Equations and its relation to Mathematical General Relativity , in specific, mathematical study of Einstein field equations in vacuum, its solutions, their stability, conservations laws, global existence solution, cosmological-type solution, as well as Virial method for the study of asymptotic behavior of the gravitational wave type solitonic solutions.
Publications
Global Existence and Long Time Behavior in Einstein-Belinski-Zakharov Soliton Spacetimes, with Claudio Muñoz. arXiv:2305.01414. Submitted.
Global Existence and Long Time Behavior in the 1+1 dimensional Principal Chiral Model with Applications to Solitons , Annales Henri Poincaré - A Journal of Theoretical and Mathematical Physics (2024). https://doi.org/10.1007/s00023-023-01405-y
Riccati–Ermakov systems and explicit solutions for variable coefficient reaction–diffusion equations, (with Erwin Suaso and Enrique Pereira). Applied Math. and Computation.
Research Stays
Universidad de Córdoba, Spain, with the professor Miguel A. Alejo, February 2024.
Georgia Institute of Technology, E.E.U.U., with the professor Gong Chen, December-March 2023.
Universidad de Córdoba, Spain, with the professor Miguel A. Alejo, September-October 2022.
Université Paris Saclay, France, with the professor Frédéric Roussett, June 2022.
Recent Talks
Somachi: Annual Meeting of the Mathematical Society of Chile. Universidad de Chile. December 2023.
IX Conference of Ecuadorian Mathematicians in Paris . Institut Henri Poncaré. November 2023
Congreso de Mujeres Matemáticas. WoMaths. UChile, Poster presentation. May 2023.
Jornada de la Matemática de la Zona Sur. Universidad de Concepción. April 2023.
PDE Seminar, Math. College of Science. Georgia Tech. January 2023.
Bilbao Analysis and PDE Seminar, Basque Center to Applied Math. BCAM. January 2023.
Encuentro Nacional de Estudiantes de Matemáticas, organized by PUC. Santiago, Chile. November 2022.
New trends in Mathematics oof Dispersive, Integrable and Nonintegrable Models in Fluids, waves and Quantum Physics. BIRS, Alberta, Canadá. October 2022.
Seminario del Departamento de Matemáticas, Universidad de Córdoba. Córdoba, España. September 2022.
I Congreso de Estudiantes de Postgrado fcfm, at the Universidad de Chile. Santiago, Chile. August 2022.
Seminario de Análisis y Geometría PUC, at the Universidad Católica de Chile. Santiago, Chile. July 2022.
XXXIV Jornada de Matemáticas de la Zona Sur, organized by Universidad de los Lagos. Online event. April 2022.
CMM-PDE Seminar, at the Universidad de Chile. Santiago, Chile. March 2022.
IV International Workshop on Nonlinear Analysis and Partial Differential Equations, National University of Colombia, Manizales
(Poster Presentation). July 2017.Inter-University Seminar on Mathematical Research, SIDIM XXIX, Pontifical Catholic University of Puerto Rico, Ponce PR, (Poster Presentation). 2014.
Organization of events
Co-organizer: Encuentro Latinoamericano de Estudiantes de Doctorado en Modelamiento, Ingeniería y Ciencias – EMIC 2023
Co-organizer: Encuentro de Estudiantes de Matemáticas ENEMAT 2023.
Attending Events
School on Modeling and Simulation of Gravitational Waves. CMM, Universidad de Chile.
Conference: Harmonic Analysis and Partial Differential Equations, Hausdorff Center of Mathematics, Universitat Bonn,
Young Researcher’s Workshop on Nonlocal PDEs and Applications , Facultad de Ciencias , Universidad de Granada,
Summer School on Fluids and Turbulence, Institut Camille Jordan , University of Lyon 1 Claude Bernard,
Conference en Hommagé a Jean Ginibre, Mathematical Institute of Orsay, Université- Paris-Saclay,
French Latin-American Conference on New Trends in Applied Mathematics (FLACAM), University of Chile, Santiago (CL)
Harmonic Analysis & Partial Differential Equations, Recent Developments & Future Directions, A conference in honor of C.E.Kenig, The University of Chicago, Chicago IL. Funded: National Science Foundation (NSF). 2014
Advancing Chicanos/Hispanic & Native Americans in Science, SACNAS National Conference, USA, San Antonio TX. 2013
Advancing Chicanos/Hispanic & Native Americans in Science , SACNAS National Conference, USA, Seattle WA. 2012
Teaching experience
As an assistant professor in the Unversity of Chile
In the courses: Calculus in Several Variables, Topology and Real Analysis, Non-linear Analysis, Ordinary Differential Equations.
As full time professor in the University of Santiago de Cali.
As professor in the Pontifical University Javeriana of Cali.
As an assistant professor in the Unversity of Puerto Rico, at Mayaguez
In the courses: Precalculus and linear algebra.