We will decide on speakers for Trinity term 2024.

It is a standard result that mapping class groups of high genus do not surject the integers. This is easily shown by computing the abelianization of the mapping class group using a presentation. Once we pass to finite index subgroups, this becomes a conjecture of Ivanov. More generally, we can ask which groups admit epimorphisms from finite index subgroups of the mapping class group. In this talk, I will present a geometric approach to this question, using harmonic maps, and explain some recent results.

A wide variety of solutions have been proposed in order to cope with the deficiencies of Modern Portfolio Theory. The ideal portfolio should optimise the investor’s expected utility. Robustness can be achieved by ensuring that the optimal portfolio does not diverge too much from a predetermined allocation. Information geometry proposes interesting and relatively simple ways to model divergence. These techniques can be applied to the risk budgeting framework in order to extend risk budgeting and to unify various classical approaches in a single, parametric framework. By switching from entropy to divergence functions, the entropy-based techniques that are useful for risk budgeting can be applied to more traditional, constrained portfolio allocation. Using these divergence functions opens new opportunities for portfolio risk managers. This presentation is based on two papers published by the BNP Paribas QIS Lab, `The properties of alpha risk parity’ (2022, Entropy) and `Turning tail risks into tailwinds’ (2020, The Journal of Portfolio Management).