Week 29.01.2023 – 04.02.2023

These lectures aim to provide a self-contained introduction to the modern conformal bootstrap method. The study of conformal field theory (CFT) will first be motivated and the “old” way of studying CFTs as endpoints of RG flows will be explained. The set of ideas necessary to understand the conformal bootstrap method will then be introduced, and both analytic and numerical implementations of the conformal bootstrap method will be discussed.

G-Research are a leading quantitative research and technology company based in London. Day to day we use a variety of quantitative techniques to predict financial markets from large data sets worldwide. Mathematics, statistics, machine learning, natural language processing and deep learning is what our business is built on. Our culture is academic and highly intellectual. In this seminar I will explain our background, current AI research applications to finance and our ongoing outreach and grants programme. The seminar will be aimed at PhD and Masters students who are curious about quant finance or interested in internship opportunities. The presentation will be of a duration of 45 minutes with 15 minutes for Q&A. We will cover the following topics: Introducing G-Research What happens in the black box? What does a Quant look like? Our recruitment and internship processes Q&A Bio: Dr Charles Martinez is the Academic Relations Manager at G-Research. Charles started his studies as a physicist at University Portsmouth Physics department's MPhys programme, and later completed a PhD in Phonon interactions in Gallium Nitride nanostructures at the University of Nottingham. Charles then worked on indexing and abstract databases at the Institution for Engineering and Technology (IET) before moving into sales in 2010. Charles' previous role was as Elsevier's Key Account Manager, managing sales and renewals for the UK Russell Group institutions, Government and Funding body accounts, including being one of the negotiators in the recent UK ScienceDirect Read and Publish agreement. Since leaving Elsevier Charles is dedicated to forming beneficial partnerships between G-Research and Europe's top institutions, and is living in Cambridge, UK. ​​

Topological recursion has become known as a powerful recursive formalism to compute a variety of invariants in mathematics and physics. The list of applications includes matrix model correlation functions, 2d gravity amplitudes, topological string theory amplitudes, and more. Interestingly, recent study has shown that by introducing the notion of Airy structures, topological recursion can be described in terms of twisted representations of the Virasoro algebra. In this talk, I will first give an introductory overview of topological recursion as well as Airy structures. Then, I will present how one can generalise the current formalism of topological recursion, e.g. by upgrading the Virasoro algebra to the super Virasoro algebra or the q-Virasoro algebra. If time permits, I will also discuss expected applications of such generalisations. This is in part joint with Vincent Bouchard and also in part joint with Nitin Chidambaram. Notice the unusual day!