Welcome to my webpage. I am currently a Fellow and College Teaching Officer at King's College, Cambridge, and thus an affiliate member in DPMMS. I also sit on the Advisory Group of the MI Garage Ethics Committee.

My main mathematical interests lie in decision problems in group theory. This is an area of study that sits at the interface between mathematical logic (more specifically: computability theory) and algebra (more specifically: group theory). In short, I find various ways of embedding the mechanical action of a Turing Machine into a group, usually reflected via group multiplication, to show that various problems in group theory are undecidable (that is, computationally impossible).

Related to this, I have interests in combinatorial and geometric group theory, computability theory, and low-dimensional topology. It is these areas that provide the tools for, and the applicaitions of, the theory of undecidability in groups.

You can find more about my research, including a list of publications, by going to my research page.

In 2016 I started looking in to the ethical issues that mathematically-trained people may face as part of their mathematical work. This covers mathematicians in academia, as well as those working in industry. I've delivered a lecture series on this, organised conferences, travelled to give seminars, have several writings, and have set up a disucssion paper series, on this. There are a team of us now working on this, under the banner of the Cambridge University Ethics in Mathematics Project (CUEiMP) which was set up in 2018. It has plenty of resources for those wanting to learn more about, or even teach, ethics in mathematics.

I have taught several courses in Cambridge, at the undergraduate and graduate levels, as well as a course on ethics in mathematics. You can find more about my teaching, including course notes, example sheets, and other resources, by going to my teaching page.

2019-present: Fellow and College Teaching Officer at King's College, University of Cambridge.

2017-2019: Faculty postdoctoral research fellow, Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, UK.

2015-2017: Marie SkÅ‚odowska-Curie postdoctoral research fellow, Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, UK.

2013-2015: Postdoctoral research fellow, Department of Mathematics, University of Neuchatel, Switzerland.

2012-2013: Postdoctoral research fellow, Department of Mathematics, University of Milan, Italy.

I have two PhDs in mathematics, from the University of Melbourne (Australia), and the University of Cambridge (UK).

**Email:**
mcc56 AT cam DOT ac DOT uk

**Office (DPMMS):** C0.07

**Office (King's):** P1, Webb's Court.

**Postal Address (DPMMS):** Centre for Mathematical Sciences, Wilberforce Road, Cambridge, CB3 0WB, UK.

**Postal Address (King's):** King's College, King's Parade, Cambridge, CB2 1ST, UK.

**Telephone (DPMMS):** +44 (0)1223 765914