Lucas M. Moschen

Hi, I’m Lucas, a PhD student in Mathematics at Imperial College London, working with Greg Pavliotis and Dante Kalise. I like problems that let me move between differential equations, probability, control, and coding to see what is going on.

These days, I spend much of my time thinking about how to change probability distributions over time. In particular using feedback control. This takes me through Fokker-Planck and McKean-Vlasov equations, Wasserstein gradient flows, interacting particles, and sampling. There is plenty to keep me occupied between proving that a control works and making it work in a computation!

You can find the different threads of this work on my Projects page, and the papers on Publications.

My story with mathematics

Mathematics became part of my life quite early, through the Brazilian Mathematical Olympiad of Public Schools (OBMEP). It brought me my first mathematical awards and introduced me to the junior scientific initiation programme, PIC. Back then, the problems were about algebra, number theory, and geometry. The subjects I work on have changed quite a bit since then, but that was where this story began.

At FGV in Rio de Janeiro, I studied Applied Mathematics and worked with Luiz Max Carvalho on statistical inference: how to estimate disease prevalence when a sampling method is not straightforward and the diagnostic tests are imperfect. For my master’s, I worked with Maria Soledad Aronna on vaccination strategies in networks of cities. Questions about who travels where, and how many vaccines are available, became questions about ODEs and optimal control.

My next stop was a second master’s at Sorbonne University, where I worked with Camille Coron and Luis Almeida on stochastic models and control of mosquito populations. Now I’m in London, working on the control of probability distributions more broadly. Epidemics, mosquitoes, and interacting particles have given me different ways of thinking about how local behaviour adds up to a collective picture.

Along the way, I’ve been supported by the PICME Scholarship, the CDMC Talent Program, and the PGSM Master Scholarship from FSMP. My PhD is supported by the Roth PhD Scholarship under the CNRS–Imperial Joint Program. I’m grateful for the people and programmes that have made these steps possible.

For dates and the more formal version, there is my CV.

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