# Mathematics Institute

About me: I am a fourth year PhD student, supervised by Dr Marco Schlichting. Previously, I attended the University of Glasgow, graduating in 2016 with an MSci in Pure Mathematics. I am originally from Glasgow. My workroom is B0.15, and my email address is d (dot) madden (at) warwick (dot) ac (dot) uk.

Research interests: My current research interests are in higher Grothendieck-Witt theory, also known as Hermitian K-theory, which is a generalization of algebraic K-theory. In algebraic K-theory, given a ring $R$, one studies a series of abelian groups $K_n(R)$, which encode information about $R$. In Hermitian K-theory, we consider rings $R$ with involution, and study a series of abelian groups $K_n^h(R)$ which encode information about $R$, including the structure of its involution. This has applications, for example, to A1 homotopy theory, which is a method for applying topological techniques to algebraic geometry; for instance, in A1 homotopy theory, the affine line plays a role analogous to that of the interval $[0,1]$ in topology.

In the past, during my Masters year at Glasgow, I worked on cyclic homology with Dr Ulrich Kraehmer.

Talks:

• Cyclic vs mixed homology, Postgraduate Seminar, University of Warwick, January 2018.
• Getting What You Pay For: An Introduction to Algebraic K-theory, Young Mathematicians Colloquium, University of Birmingham, April 2018.

Papers:

• Cyclic vs mixed homology (Joint work with Ulrich Kraehmer) Homology, Homotopy, and Applications, vol.20 (1), 2018, pp.237-250

Other writings: