Hydrodynamics allow for efficient computation of many-body dynamics and have been successfully used in the study of black hole horizons, collective behaviour of QCD matter in heavy ion collisions, and non-equilibrium behaviour in strongly-interacting condensed matter systems.
In this talk, I will present the application of hydrodynamics to quantum field theory with an infinite number of local conservation laws. Such an integrable system can be described within the recently developed framework of generalised hydrodynamics. I will present the key assumptions of generalised hydrodynamics as well as summarise some recent developments in this field. In particular, I will concentrate on the study of the SU(3)_2-Homogeneous sine-Gordon model. Thanks to the hydrodynamic approach, we were able to identify the key dynamical signatures of unstable excitations in this integrable quantum field theory and simulate the real time RG-flow of the theory between interacting and free conformal regimes.
The talk is based on joint work with Olalla Castro-Alvaredo, Cecilia De Fazio and Benjamin Doyon.

We present a framework to generate and evaluate thematic recommendations based on multilayer network representations of knowledge graphs (KGs).  We represent the relative importance of different types of connections (e.g., Directing/acting) with an intuitive salience matrix that can be learnt from data, tuned to incorporate domain knowledge, address different use cases, or respect business logic. We apply an adaptation of the personalised PageRank algorithm to multilayer network models of KGs to generate item-item recommendations. These recommendations reflect the knowledge we hold about the content, and are suitable for thematic or cold-start settings.

Evaluating thematic recommendations from user data presents unique challenges. Our method only recommends items that are 'thematically' related; that is, easily reachable following connections in the KG. We develop a variant of the widely-used Normalised Discounted Cumulative Gain (NDCG) to evaluate recommendations based on user-item ratings, respecting their thematic nature.

We apply our methods to a KG of the movie industry and MovieLens ratings and in an internal AB test. We learn the salience matrix and demonstrate that our approach outperforms existing thematic recommendation methods and is competitive with collaborative filtering approaches.

The notion of topological order was introduced by Xiao-Gang Wen in order to capture the features of the exotic phases of matter given by fractional quantum Hall phases. I will motivate why the corresponding mathematical structures are higher categories with additional properties. In 2+1-dimensions, I will explain in details how the definition of fusion category arises from physical and geometrical intuitions about topological orders. Finally, I will sketch how the notion of higher fusion category emerges in higher dimensions.

Representations of finite reductive groups have a rich, well-understood structure, first explored by Deligne--Lusztig. In joint work with Anne-Marie Aubert and Dan Ciubotaru, we show a way to lift some of this structure to representations of p-adic groups. In particular, we consider the relation between Lusztig's nonabelian Fourier transform and a certain involution we define on the level of p-adic groups. This talk will be an introduction to these ideas with a focus on examples.

I will explain how various results in arithmetic statistics by Bhargava, Gross, Shankar and others on 2-Selmer groups of Jacobians of (hyper)elliptic curves can be organised and reproved using the theory of graded Lie algebras, following earlier work of Thorne. This gives a uniform proof of these results and yields new theorems for certain families of non-hyperelliptic curves. I will also mention some applications to rational points on certain families of curves.