About
Hi! I am María, a 1st-year Mathematics DPhil student at the University of Oxford supervised by Prof. Renaud Lambiotte, Prof. Irene Moroz, and Dr Scott Osprey. In my research, I use applied mathematics techniques to explore atmospheric phenomena. Recently I have been focusing on using networks to analyse stratospheric flow. However, I have a broad range of interests like
- non-linear dynamics, bifurcation theory, and chaos theory;
- mathematical modelling of atmospheric phenomena;
- numerical solutions to partial differential equations;
- and, graph theory.
Studies
I completed a BSc in Physics at King's College London with an average above 85%. Fully funded by a Fundación Barrié Overseas Postgraduate Scholarship, I moved to Oxford to pursue an MSc in Mathematical Modelling and Scientific Computing. I was awarded a distinction for both my dissertation and award classification. Currently, I've been granted an UKRI EPSRC Scholarship to undertake a DPhil at Oxford's Mathematical Institute in OCIAM (Oxford Centre for Industrial and Applied Mathematics).
DPhil Thesis
The atmosphere is a complex system in which large-scale interactions between different flow elements give rise to collective behaviours. Extracting these features from atmospheric data remains challenging due to the methodological constraints imposed by high dimensionality, multi-scale dynamics, and non-linearity.
In my thesis, I study how complex networks can be used to uncover these relationships by simplifying continuous flow data into more tractable discrete graphs. Graph theory allows us to reveal the topology of the connectivity patterns, quantify the influence of individual flow elements on the overall dynamics, cluster the flow into groups with similar characteristics, etc. I will explore how these structures can be used to characterise the system dynamics, benchmark models, and feedback in the modelling.
Feel free to contact me with any ideas or collaboration requests.
Fig. Simulation of the winter stratospheric polar vortex undergoing a sudden stratospheric warming event. (Left) Potential vorticity. (Right) The extent to which the vorticity at a point induces velocity to the flow.
Other
When I’m not staring at code, you can find me oil painting, reading novels, watching movies, running, or attempting to play tennis.