The Landau paradigm of phase transitions states that any continuous (second order) phase transition is a symmetry breaking transition. Originally this was formulated for symmetries that form groups, e.g. the critical Ising model is the transition between the $\mathbb{Z}_2$ symmetric and spontaneously broken phases. In recent years a new class of symmetries, called categorical or non-invertible, have emerged in quantum systems -- with impact ranging from high energy and condensed matter physics to mathematics, and quantum computing. I will explain how these symmetries generalize the Landau paradigm and how new phases and phase transitions are predicted, which have potential future experimental implementations in cold atom systems.

The seminar has been cancelled.

I will discuss recent developments in constructions of 5d N=1 supersymmetric gauge theories and their UV fixed points, which are strongly-coupled SCFTs. The lectures will start with some background on 5d gauge theories, their Coulomb branch and effective action, as well as their constructions in M-theory on non-compact Calabi-Yau threefolds. In the second lecture I will discuss some new developments of various groups in the past year.

String theory phenomenology generically suffers from either too much flexibility (and lack of predictability) or from the a high specialization to case by case studies. I will discuss how F-theory GUT model building manages to get around these pitfall, in particular, I will explain, how to systematically include global string consistency conditions, which are independent of the specific compactification, and which come with the benefit of highly constraining the class of GUT models that can arise from F-theory.

I will give an overview of recent developments in F-theory GUT model building. First I will discuss the basic ideas of F-theory model building, exemplifying this by the construction of supersymmetric SU(5) GUTs. Then I will outline how global string theoretic consistency requirements impact the SUSY phenomenology. The main focus of this talk will be on the phenomenological implications of these models.