Dr Stacey Law

Photo of Dr Stacey Law

MMath, MA, PhD (Cantab)

Research Fellow

I was born and grew up in Sydney, Australia, though you might not be able to tell from my accent nowadays, since I came to Cambridge in 2011 to study mathematics at Trinity College. Following my BA and MMath, I continued at the Department of Pure Mathematics and Mathematical Statistics in Cambridge for my PhD, after which I was a London Mathematical Society Early Career Fellow at the University of Oxford. Having spent many wonderful years in Cambridge, I'm thrilled to have returned to join the Emmanuel community. I am excited and grateful for the opportunity, as the Meggitt Research Fellow, to develop my academic research as well as to be involved in Direction of Studies at Emmanuel, helping to guide and inspire students in mathematics.

My main research area is the representation theory of finite groups, particularly the symmetric groups, related objects such as the Schur algebras, and algebraic combinatorics. Symmetries exist all around us, playing an active role in the way we process information: they help us filter data efficiently in order to simplify and solve complex problems. In order to study symmetries systematically, an abstract mathematical framework known as group theory was developed, with the aim of modelling symmetries by, for instance, codifying them into mathematical objects such as groups and algebras, and then understanding their structure. At its core, representation theory is the study of how these objects act: by understanding how they interact with other objects, we can learn more about their structure than from looking at groups and algebras in isolation.

The primary focus of my research is on the symmetric groups, a widely-studied family of finite groups occurring in all areas of science. My current research is partly motivated by the Local-Global Conjectures, a family of open problems lying at the heart of modern representation theory, so named because of the recurring theme: to study the global structure of a complicated group, it is often enough to zoom in and understand the local structure of a smaller fraction of the group. The local information is enough, thanks to symmetry, to determine the desired information at the global level. In particular, my recent work concerns the relationship between so-called irreducible characters of symmetric groups and linear characters of their Sylow subgroups.

Outside of mathematics, I enjoy playing volleyball, badminton, and cycling. I would also like to find more time to continue learning Japanese, as well as pick up a number of other languages.