About me

Currently, I am working as a postdoctoral researcher in the department of mathematics at the University of Toronto. I obtained my Ph.D. in mathematics at the Université de Tours (Tours, France) in 2022, working under the advice of Prof. Luc Molinet. Previously, in 2019, I obtained my master's degree at the Université Paris-Sud (Orsay, France), where I worked with Prof. Yvan Martel on my Mémoire. In 2018, I received my bachelor's degree in Mathematical Engineering from Universidad de Chile (Santiago, Chile) under the advice of Prof. Claudio Muñoz.

Photo of Iquique, the city where I was born. None of the photos on this website are mine, I'm a terrible photographer. Although I have some very similar, but bad.

My research interest

I am mostly interested in Nonlinear dispersive equations, in particular: stability and asymptotics of solitons, long-time behavior of solutions, local well-posedness, and blow-up. Eventually, I would like to learn more about Fluid Dynamics.

Photo of the Hôtel de Ville of Tours.

Publications

13.- Local Energy control in the presence of a zero-energy resonance (in collaboration with Fabio Pusateri).

12.- Local well-posedness for the Zakharov-Kuznetsov equation on the background of a bounded function. To appear in Advances in Differential Equations.

11.- Local well-posedness for the gKdV equation on the background of a bounded function

10.- On long-time behavior of solutions of the Zakharov–Rubenchik/Benney–Roskes system (in collaboration with Maria Eugenia Martinez).

9.- Orbital stability and instability of periodic wave solutions for ϕ4n-models (in collaboration with Gong Chen).

8.- Orbital stability and instability of periodic wave solutions for the ϕ4 -model.

7.- Orbital and asymptotic stability of a train of peakons for the Novikov equation.

6.- On asymptotic stability of the sine-Gordon kink in the energy space (in collaboration with Miguel Angel Alejo and Claudio Muñoz).

5.- Asymptotic stability of peakons for the Novikov equation.

4.- Nonlinear stability of 2-solitons of the sine-Gordon equation in the energy space (in collaboration with Claudio Muñoz).

3.- Dispersive blow-up and persistence properties for the Schrödinger–Korteweg–de Vries system (in collaboration with Felipe Linares).

2.- On the variational structure of breather solutions II: Periodic mKdV equation (in collaboration with Miguel Angel Alejo and Claudio Muñoz).

1.- On the variational structure of breather solutions I: Sine-Gordon equation (in collaboration with Miguel Angel Alejo and Claudio Muñoz).

A preprint version of all my articles can be found on both ArXiv and ResearchGate