Applications of nuclear physics to a wider context: from molecules to stars passing through hypernuclei

In this contribution I will review some of the researches that are currently being pursued in Padova (mainly within the In:Theory and Strength projects), focusing on the interdisciplinary applications of nuclear theory to several other branches of physics, with the aim of contributing to show the centrality of nuclear theory in the Italian scientific scenario and the prominence of this fertile field in fostering new physics. In particular, I will talk about: i) the recent solution of the long-standing electron screening puzzle that settles a fundamental controversy in nuclear astrophysics between the outcome of lab experiments on earth and nuclear reactions happening in stars; the application of algebraic methods to very diverse systems such as: ii) the supramolecular complex H2@C60, i.e. a diatomic hydrogen molecule caged in a fullerene and iii) to the spectrum of hypernuclei, i.e. systems made of a Lambda particles trapped in (heavy) nuclei.