About

Hey! This is Ismael Leal—welcome to my personal website. I'm a graduate mathematician from the University of Oxford and currently pursuing a PhD at EPFL in the Laboratory of Fluid Mechanics and Instabilities (LFMI). Thanks to my academic and research experience, I have become proficient in several state-of-the-art mathematical & numerical methods. Some of my main areas of interest include:

• numerical solutions to partial differential equations;
• non-linear dynamics, bifurcation theory, & chaos theory;
• continuous optimisation, numerical linear algebra, & machine learning;
• graph & hypergraph theory;
• generic mathematical modelling of physical and biological systems;
• scientific software engineering, with a focus on clean architecture, testing, and performance.

Studies

I completed a BSc in Physics at King's College London with an average of 80%. Then, I moved to Oxford to pursue an MSc in Mathematical Modelling and Scientific Computing, earning a distinction in my dissertation and a merit for my award classification. I am now a PhD candidate at EPFL, working on the theoretical and numerical modelling of symmetry-breaking dynamics in fluid flows, with applications to engineering, energy, and biological systems.

Current research

During the first year of my doctoral studies, I have been exploring reduced-order models for fluids, specifically the Dynamically-Orthogonal (DO) equations. The DO equations can be applied to any stochastic system. At the moment, I have been trying to adapt the Nektar++ software so that it can solve my DO system for an arbitrary geometry using the built-in velocity-correction schemes. The goal is to simulate and explore noise-induced transitions with the DO scheme, particularly loss-of-symmetry for flows around an Ahmed body.