Gian Maria Dall’Ara: “Very degenerate linear second order PDEs from Several Complex Variables”

In this talk, I will present some recent results and open problems about global regularity properties of classes of second order PDEs with non-negative characteristic form (e.g., sum-of-squares operators) that fail to satisfy the Hörmander condition, and nevertheless appear naturally in Several Complex Variables.Part of the results that I will present are joint with S.…
Giulio Tralli: “Operators with linear drift terms with imaginary spectrum, and their Liouville properties”

In this talk we discuss the validity of Liouville theorems for non-negative solutions to hypoelliptic equations with constant diffusion and linear drift. Assuming that the drift term has imaginary spectrum, we show such one-sided Liouville property as a by-product of an invariant Harnack inequality for ancient solutions to parabolic equations of Kolmogorov type.We focus on…
Lorenzo Liverani: “A Taxonomy of Neural ODEs“

Neural Ordinary Differential Equations (Neural ODEs, or NODEs) constitute a key class of models in modern machine learning. Introduced in 2018 as a continuous-time analogue of ResNets, NODEs offer a natural framework for studying deep neural networks through tools from mathematical analysis and control theory. Since their introduction, a wide variety of NODE architectures has…

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