I have obtained my PhD at Politecnico di Milano (Italy) and I am currently a postdoctoral researcher at FAU Erlangen-Nürnberg. (Very rare picture of me wearing a tie on the left.)
My interests are focused on three main areas:
What happens to the solutions of a dynamical system as time goes to infinity? I investigate if their energy decays to zero, in which case, I study whether the decay rate is polynomial or exponential. This is the realm of semigroup theory and fine energy estimates
Working in Machine Learning is sometimes still regarded as an alchemist's job: you mix models together and see what happens. Neural ODEs give some perspective on the inner workings of a Neural Network, allowing to predict and control its behavior to a certain extent.
Spectral stability problems aim to understand how the spectrum of a differential operator change under small perturbations. I focused on singular perturbations, obtained by poking holes inside the spatial domain.
You can see the full list of my publications here: 📚 View Full Publications List
If you also like estimating stuff and staring at the blackboard, feel free to reach out!
You can contact me via email at lorenzo.liverani@fau.de