Alvaro Carballeira

I am a first-year Ph.D. student in the Department of Mathematics at Brown University, where I am advised by Javier Gómez-Serrano. My main interest is the analysis of partial differential equations. My intention is to use traditional analysis together with numerical results to build rigorous computer-assisted proofs. Most recently I have been studying some equations related to fluid mechanics and quantum-mechanical phenomena.

In 2024 I finished my Master’s degree at Univesidad Autónoma de Madrid (Spain). At the same time I had a position as a young reseracher at ICMAT. My Master’s thesis consisted on variational techniques used in phase-field modelling. Before that I did my Bachelor’s thesis on physics-informed neural networks.

Here is a copy of my CV. Last updated in February 2025.

Contact: alvaro_carballeira_mora[at]brown.edu