We will decide on speakers for Trinity term 2024.

This talk will introduce Khovanov and Knot Floer Homology as tools for studying knots. I will then cover some applications to problems in knot theory including distinguishing embedded surfaces and how they can be used in the context of ribbon concordances. No prior knowledge of either will be necessary and lots of pictures are included.

In 2006, Jan Dymara introduced the concept of weighted \(\ell^2\) Betti numbers as a method of computing regular \(\ell^2\) Betti numbers of buildings. This notion of dimension is measured by using Hecke algebras associated to the relevant Coxeter groups. I will briefly introduce buildings and then give a comparison between the regular \(\ell^2\) Betti numbers and the weighted ones.

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.

Frontiers in Quantitative Finance is brought to you by the Oxford Mathematical and Computational Finance Group and sponsored by CitiGroup and Mosaic SmartData.

Abstract
This paper parsimoniously generalizes the VIX variance index by constructing model-free factor portfolios that replicate skewness and higher moments. It then develops an infinite series to replicate option payoffs in terms of the stock, bond, and factor returns. The truncated series offers new formulas that generalize the Black-Scholes formula to hedge variance and skewness risk.


About the speaker
Steve Heston is Professor of Finance at the University of Maryland. He is known for his pioneering work on the pricing of options with stochastic volatility.
Steve graduated with a double major in Mathematics and Economics from the University of Maryland, College Park in 1983, an MBA in 1985 followed by a PhD in Finance in 1990. He has held previous faculty positions at Yale, Columbia, Washington University, and the University of Auckland in New Zealand and worked in the private sector with Goldman Sachs in Fixed Income Arbitrage and in Asset Management Quantitative Equities.

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).