While the world was reopening after gloomy pandemic-times, my visit at the ICL, for a semester in 2022-2023, felt like a most-welcome breath of fresh air. London's high academic standards in general and, the incipient collaboration with my host Dr. Sheehan Olver in particular, meant both a great challenge and opportunity for my work on rigorous numerics. This field aims at bridging the gap between experimental mathematics and computer proofs by guaranteeing the numerical accuracy of computations. Relevant examples range from theoretical proofs in dynamical systems to practical engineering problems like the control of spacecraft engines.
With Dr. Olver, we worked on developing efficient and reliable spectral methods for solving specific classes of ODEs, integration or optimization problems which can be reformulated as infinite-dimensional systems of linear equations, with a sparse banded-like structure. To certify the existence (and uniqueness) of solutions we made-use of a Newton-like method, with underlying set-based operations, like interval or ball arithmetic.
During my visit, I gave a short master/PhD level course, which provided an introduction to the basic tools of my field and stimulated some interesting discussions with members of the Dynamical Systems group at ICL. I also got the chance to attend several seminars and conferences on topics related to our research (ranging from differential algebra to a Julia software expert meetup).
The length of this visit was sufficient to establish a solid common ground and advance on several ideas, both with Dr. Olver and several of his collaborators. I am confident that our collaboration will continue to bring this project to fruition.
Host: Dr Sheehan Olver
