A group acting on a regular rooted tree has the congruence subgroup property if every subgroup of finite index contains a level stabilizer. The congruence subgroup problem then asks to quantitatively describe the kernel of the surjection from the profinite completion to the topological closure as a subgroup of the automorphism group of the tree. We will study the congruence subgroup property for a family of branch groups whose construction generalizes that of the Hanoi Towers group, which models the game “The Towers of Hanoi".

 

The social sciences are undergoing a profound shift as new data and methods emerge to study human behaviour. These data offer tremendous opportunity but also mathematical and statistical challenges that the field has yet to fully understand. This talk will give an overview of social data science research faculty are undertaking at the Oxford Internet Institute, a multidisciplinary department of the University. Projects include studying the flow of information across languages, the role of political bots, and volatility in public attention.

We will talk about set theory, and, more specifically, forcing. Forcing is powerful. It is the go-to method for proving the independence of the continuum hypothesis or for understanding the (lack of) fine structure of the real numbers. However, forcing is hard. Keen to export their theorems to more mainstream areas of mathematics, set theorists have tackled this issue by inventing forcing axioms, (relatively) simple mathematical statements which describe sophisticated forcing extensions. In my talk, I will present the basics of forcing, I will introduce some interesting forcing axioms and I will show how these might be used to obtain surprising independence results.

This will be the final mathematrix meeting for the term and we will be discussing Implicit Bias. In short, Implicit Bias is to do with perceptions and judgements we unconsciously make about people based on preconceptions we have about certain appearances, background or other characteristics. Even if we are not aware of making these judgements, they can affect our actions and decisions none-the-less. For a slightly longer introduction about this topic and how it can relate to academia, we suggest reading the following article: http://science.sciencemag.org/content/352/6289/1067.full

In this session we hope to explain more about what implicit bias is, how it might affect us, and discuss ways to avoid implicit bias and make ourselves and others more aware of it.

Everyone is welcome! Monday, 1300-1400, Quillen Room (N3.12), with lunch provided.

Partition Lie algebras are generalisations of rational differential graded Lie algebras which, by a recent result of Mathew and myself, govern the formal deformation theory of algebro-geometric objects in finite and mixed characteristic. In this talk, we will take a closer look at these new gadgets and discuss some of their applications in algebra and topology