Looking for a delicious, healthy start to your day? We’re excited to announce the launch of our Yoghurt Bar at Café π.
Starting 30th September, join us every Monday to Friday from 8:30 am to 11:00 am for a serving of creamy natural yoghurt topped with your choice of three delicious toppings - all for just £2.60.
18:00
Backtesting with correlated data
Abstract
The important problem of backtesting financial models over long horizons inevitably leads to overlapping returns, giving rise to correlated samples. We propose a new method of dealing with this problem by decorrelation and show how this increases the discriminatory power of the resulting tests.
About the speaker
Nikolai Nowaczyk is a Risk Management & AI consultant who has advised multiple institutional clients in projects around counterparty credit risk and xVA as well as data science and machine learning.
Nikolai holds a PhD in mathematics from the University of Regensburg and has been an Academic Visitor at Imperial College London.
Registration for in-person attendance is required in advance.
15:30
A Mean Field Game approach for pollution regulation of competitive firms
Abstract
We develop a model based on mean-field games of competitive firms producing similar goods according to a standard AK model with a depreciation rate of capital generating pollution as a byproduct. Our analysis focuses on the widely-used cap-and-trade pollution regulation. Under this regulation, firms have the flexibility to respond by implementing pollution abatement, reducing output, and participating in emission trading, while a regulator dynamically allocates emission allowances to each firm. The resulting mean-field game is of linear quadratic type and equivalent to a mean-field type control problem, i.e., it is a potential game. We find explicit solutions to this problem through the solutions to differential equations of Riccati type. Further, we investigate the carbon emission equilibrium price that satisfies the market clearing condition and find a specific form of FBSDE of McKean-Vlasov type with common noise. The solution to this equation provides an approximate equilibrium price. Additionally, we demonstrate that the degree of competition is vital in determining the economic consequences of pollution regulation.
This is based on joint work with Gianmarco Del Sarto and Marta Leocata.
The Art of Cancer Modelling
Mark Chaplain is the Gregory Chair of Applied Mathematics at the University of St. Andrews.
Here's a little about his research from the St. Andrews website:
Research areas
Cancer is one of the major causes of death in the world, particularly the developed world, with around 11 million people diagnosed and around 9 million people dying each year. The World Health Organisation (WHO) predicts that current trends show the number rising to 11.5 million in 2030. There are few individuals who have not been touched either directly or indirectly by cancer. While treatment for cancer is continually improving, alternative approaches can offer even greater insight into the complexity of the disease and its treatment. Biomedical scientists and clinicians are recognising the need to integrate data across a range of spatial and temporal scales (from genes through cells to tissues) in order to fully understand cancer.
My main area of research is in what may be called "mathematical oncology" i.e. formulating and analysing mathematical models of cancer growth and treatment. I have been involved in developing a variety of novel mathematical models for all the main phases of solid tumour growth, namely: avascular solid tumour growth, the immune response to cancer, tumour-induced angiogenesis, vascular tumour growth, invasion and metastasis.
The main modelling techniques involved are the use and analysis of nonlinear partial and ordinary differential equations, the use of hybrid continuum-discrete models and the development of multiscale models and techniques.
Much of my current work is focussed on what may be described as a "systems approach" to modelling cancer growth through the development of quantitative and predictive mathematical models. Over the past 5 years or so, I have also helped develop models of chemotherapy treatment of cancer, focussing on cell-cycle dependent drugs, and also radiotherapy treatment. One of the new areas of research I have started recently is in modelling intracellular signalling pathways (gene regulation networks) using partial differential equation models.
The long-term goal is to build a "virtual cancer" made up of different but connected mathematical models at the different biological scales (from genes to tissue to organ). The development of quantitative, predictive models (based on sound biological evidence and underpinned and parameterised by biological data) has the potential to have a positive impact on patients suffering from diseases such as cancer through improved clinical treatment.
Further details of my current research can be found at the Mathematical Biology Research Group web page.
Abstract
In this talk we will provide an overview of a number of mathematical models of cancer growth and development - gene regulatory networks, the immune response to cancer, avascular solid tumour growth, tumour-induced angiogenesis, cancer invasion and metastasis. In the talk we will also discuss (the art of) mathematical modelling itself giving illustrations and analogies from works of art.
15:30
Building surfaces from equilateral triangles
Abstract
The answer in the compact case is given by a famous classical theorem of Belyi, which states that a compact surface is equilaterally triangulable if and only if it is defined over a number field. These *Belyi surfaces* - and their associated “dessins d’enfants” - have found applications across many fields of mathematics, including mathematical physics.
In joint work with Chris Bishop, we give a complete answer of the same question for the case of infinitely many triangles (i.e., for non-compact Riemann surfaces). The talk should be accessible to a general mathematical audience, including postgraduate students.