Anomalies characterize the breaking of a classical symmetry at the quantum level. They play an important role in quantum field theories, and constitute robust observables which appear in various contexts from phenomenological particle physics to black hole microstates, or to classify phases of matter. The anomalies of a d-dimensional QFT are naturally encoded via descent equations into the so-called anomaly polynomial in (d+2)-dimensions. The aim of this seminar is to review the descent procedure, anomaly polynomial, anomaly inflow, and in particular their realisation in M-theory. While this is quite an old story, there has been some more recent developments involving holography that I'll describe if time permits. 

Junior Strings is a seminar series where DPhil students present topics of common interest that do not necessarily overlap with their own research area. This is primarily aimed at PhD students and post-docs but everyone is welcome.

The Landau equation stands as one of the fundamental equations in kinetic theory and plays a key role in plasma physics. However, computing it presents significant challenges due to the complexity of the Landau operator,  the dimensionality, and the need to preserve the physical properties of the solution. In this presentation, I will introduce deep learning assisted particle methods aimed at addressing some of these challenges. These methods combine the benefits of traditional structure-preserving techniques with the approximation power of neural networks, aiming to handle high dimensional problems with minimal training. 

It is well known that the theory of differential-difference fields in characteristic zero has a model companion. Here by a differential-difference field I mean a field with a differential and a difference structure where the operators commute (in other words the difference structure is a differential-endomorphism). The theory DCFA_0 was studied in a series of papers by Bustamante. In this talk I will address the case of positive characteristic.