My research focuses in nonlinear dispersive equations. In particular my main works include three branches: the study of existence and properties of solutions to models posed on the line, the study of existence and (in)stability of Schrödinger and Airy-type operators on metric graphs and controllability of Airy-type equations on metric graphs.

My particular topics of interest include:

• The study persistence of solutions in weighted Sobolev spaces for dispersive models posed on Euclidean spaces. Including the study of the optimal relation between polynomial decay and regularity.

• The study of dispersive blow-up of solutions on Euclidean space.

• The extension theory of self-adjoint/dissipative realizations of Airy and Laplace's operators on metric graphs.

• (In)stability of stationary solutions/standing waves of Schrödinger and Korteweg-de Vries equations posed on non-compact metric graphs.

• The stabilization and controllability of Kortweg-de Vries equations on non-compact metric graphs.

In case you might be wondering how I ended up here...

For my undergraduate thesis, I worked on second-order elliptic partial differential equations under the supervision of Prof. Carlos Augusto Vélez López.

In 2015, during my master’s studies, I began focusing on nonlinear dispersive equations. Under the advisory of Prof. José Manuel Jiménez Urrea, I studied the persistence of solutions in weighted Sobolev spaces for the classical Korteweg–de Vries (KdV) equation. Although a related result for KdV had already been established, I developed an alternative approach to obtain the theorem.

In 2019, I started my PhD at the Universidade Estadual de Campinas under the supervision of Prof. Ademir Pastor Ferreira. During the first year, I returned to the same general problem, now in the context of the two-dimensional Zakharov–Kuznetsov (2D-ZK) equation, inspired by an article of my former M.Sc. advisor.

With the arrival of the COVID-19 pandemic in 2020, the Brazilian dispersive equations group launched an online seminar, which became a fertile source of ideas. In particular, I was motivated to extend both my master’s thesis results and the 2D-ZK work to a more general framework. A few months later, my first article on local well-posedness for several dispersive models began to take shape. Following suggestions from my advisor, we further applied the developed theory to the study of dispersive blow-up phenomena. You can see my first article pusblised here.

The natural continuation of this line of research began in late 2021, as academic activity gradually resumed after the pandemic. I became interested in the optimality of the relationship between regularity and decay established in my earlier work. I initially explored this question for the Kawahara equation and the Hirota–Satsuma system, obtaining partial positive results. Later, by revisiting the existing persistence theory for KdV, we were able to adapt and slightly improve the argument in the modified KdV (mKdV) setting; this work is currently under peer review.

Fortunately, many related problems remain open and offer promising directions for future research. I included several of them in the final chapter of my PhD thesis, and I would be very happy to discuss any of these topics further.