Undergraduate courses in quantum mechanics pay a lot of attention to the rules for measurement, often presented in terms of an instantaneous collapse of the state vector. Meanwhile, undergraduate courses in special relativity make a point of the relativity of simultaneity. With this in mind, one might expect that courses in quantum field theory (QFT), which combines quantum theory and relativity, would address this apparent contradiction - but instead one encounters silence on the matter. In this lecture I will explain why the topic of measurement in quantum field theory presented more problems than solutions for many years, and describe a recently developed framework that clarifies how (and why) states should be updated in QFT following measurements, and which has among other things resolved the long-standing problem of "impossible measurements". The framework fits within an approach to QFT called algebraic quantum field theory, which I will explain. No prior knowledge of QFT will be assumed. 

Corso di formazione e aggiornamento per docenti di matematica, fisica e scienze delle scuole secondarie superiori

Dissipative phase transitions (DPTs) have emerged as a central paradigm for understanding critical phenomena in driven open quantum systems. Their characterisation is traditionally based on the spectral properties of a time-independent Liouvillian, an approach that becomes inadequate for genuinely time-periodic (Floquet) systems. In this talk, a general framework will be presented for the study of DPTs in periodically driven open quantum systems based on the spectrum of the Floquet propagator. Using driven-dissipative Kerr resonators as a first example, this framework will show how counter-rotating terms modify the location of the critical point and strongly affect the dynamical time scales associated with the transition. Dissipative criticality in the driven quantum Rabi model will then be discussed, alongside a comparison with the driven Jaynes–Cummings approximation. This analysis reveals qualitative changes in the critical properties as the ultrastrong light–matter coupling regime is approached and demonstrates the eventual disappearance of the DPT in the deep-strong-coupling regime as a consequence of light–matter decoupling. These results establish a rigorous framework for exploring dissipative critical phenomena beyond the time-independent setting and open new avenues for the study of nonequilibrium phase transitions in periodically driven quantum systems.

The anomalous magnetic moment of the muon represents one of the most stringent tests of the Standard Model of particle physics. Thanks to both extremely precise theoretical calculations and high-precision measurements, this quantity provides a unique window into possible effects of physics beyond the Standard Model.
In the first part of the seminar, the concept of the muon magnetic moment and its anomalous contribution will be introduced. The quantum origin of the anomaly will be discussed, showing how electromagnetic, weak, and hadronic interactions contribute to the theoretical prediction of (g-2). The role of possible contributions from new physics will also be highlighted, together with the current Standard Model prediction and its uncertainties.
The second part of the seminar will focus on the experimental determination of the muon anomalous magnetic moment, with particular emphasis on the Fermilab Muon (g-2) experiment. The storage ring technique will be presented, together with alternative approaches which include a search for the muon electric dipole moment. The latest experimental results and their implications for searches for new physics will be discussed, as well as the future of this field of research.

Evaluating the reliability of machine learning classifications remains a fundamental challenge in Artificial Intelligence (AI), particularly when the target variable is multidimensional. Classification variables can be expressed by means of a categorical scale which, at best, is ordinal. Because ordinal data lack a natural metric structure in their underlying space, most conventional distance measures aimed at assessing the accuracy of machine learning classifications cannot be directly or meaningfully applied. In the talk, we develop a mathematical framework for comparing ordinal data based on a family of Rank Graduation (RGXp) metrics. We demonstrate that these metrics can quantify the proportion of variability of the response explained by the predictions, in a similar manner as the predictive R^2 for continuous response variables. After establishing theoretical connections between the RGXp family and other prominent metrics in AI, we conduct extensive experiments across diverse datasets and learning tasks to evaluate their empirical performance. The results underscore the versatility, interpretability, and robustness of the RGXp metrics as a principled foundation for developing trustworthy and SAFE AI systems. The results also show the potential of hybrid quantum machine learning models, which seem to improve the robustness of the results.