This is a joint GR-QFT seminar, to celebrate in advance the 90th birthday of Roger Penrose later in the summer, comprising 9 talks on conformal cyclic cosmology.  The provisional schedule is as follows:

11:00 Roger Penrose (Oxford, UK) : The Initial Driving Forces Behind CCC

11:10 Paul Tod (Oxford, UK) : Questions for CCC

11:20 Vahe Gurzadyan (Yerevan, Armenia): CCC predictions and CMB

11:30 Krzysztof Meissner (Warsaw, Poland): Perfect fluids in CCC

11:40 Daniel An (SUNY, USA) : Finding information in the Cosmic Microwave Background data

11:50 Jörg Frauendiener (Otago, New Zealand) : Impulsive waves in de Sitter space and their impact on the present aeon

12:00 Pawel Nurowski (Warsaw, Poland and Guangdong Technion, China): Poincare-Einstein expansion and CCC

12:10 Luis Campusano (FCFM, Chile) : (Very) Large Quasar Groups

12:20 Roger Penrose (Oxford, UK) : What has CCC achieved; where can it go from here?

We introduce the notion of systolic complexes and give conditions on presentations to construct such complexes using Cayley graphs.

We consider Garside groups to find examples of groups admitting such a presentation.
 

The goal of this talk is to present some elementary examples of fusion 2-categories whilst doing as little higher category theory as possible. More precisely, it turns out that up to a canonical completion operation, certain higher fusion categories are entirely described by their maximal subspaces. I will briefly motivate this completion operation in the 1-categorical case, and go on to explain why working with spaces is good enough in this particular case. Then, we will review some fact about $E_n$-algebras, and why they come into the picture. Finally, we will have a look at some small examples arising from finite groups.

Techniques that address sequential data have been a central theme in machine learning research in the past years. More recently, such considerations have entered the field of finance-related ML applications in several areas where we face inherently path dependent problems: from (deep) pricing and hedging (of path-dependent options) to generative modelling of synthetic market data, which we refer to as market generation.

We revisit Deep Hedging from the perspective of the role of the data streams used for training and highlight how this perspective motivates the use of highly-accurate generative models for synthetic data generation. From this, we draw conclusions regarding the implications for risk management and model governance of these applications, in contrast to risk management in classical quantitative finance approaches.

Indeed, financial ML applications and their risk management heavily rely on a solid means of measuring and efficiently computing (similarity-)metrics between datasets consisting of sample paths of stochastic processes. Stochastic processes are at their core random variables with values on path space. However, while the distance between two (finite dimensional) distributions was historically well understood, the extension of this notion to the level of stochastic processes remained a challenge until recently. We discuss the effect of different choices of such metrics while revisiting some topics that are central to ML-augmented quantitative finance applications (such as the synthetic generation and the evaluation of similarity of data streams) from a regulatory (and model governance) perspective. Finally, we discuss the effect of considering refined metrics which respect and preserve the information structure (the filtration) of the market and the implications and relevance of such metrics on financial results.