Events

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…

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…

The workshop “Semigroups, Evolution Equations and Positivity” on the occasion of Rainer Nagel’s 85th birthday has been held at the University of Siena in December 3-5, 2025. The Italian-German collaboration in the field of functional analysis—with a particular focus on evolution equations, operator semigroups, and positivity—was initiated by Edoardo Vesentini and Giuseppe Da Prato in…