I am a lecturer at the University of Glasgow in both the Geometry and Topology group and the Algebra group. Prior to this I was a postdoc with Prof. Michael Weiss at the Westfaelische Wilhelms-Universitaet Muenster and a postdoc at the Max Planck Institute for Mathematics in Bonn. I completed my Ph.D. under the supervision of Prof. Andrew Ranicki at the University of Edinburgh. I am mostly interested in the following branches of mathematics: Geometric Topology, Algebraic Topology, Controlled Topology, Algebraic and Geometric Surgery theory and Algebraic K-Theory.

## Research Interests

For X a (finite) simplicial complex that is homotopy equivalent to a manifold the topological surgery exact sequence of X can be identified with the algebraic surgery exact sequence of X. The latter sequence, due to Ranicki, is defined using simplicially controlled categories. I seek to generalise the algebraic subdivision functor defined in my Ph.D. thesis to the L-theory of simplicially controlled categories thereby defining a mapping of algebraic surgery exact sequences: ASES(X) --> ASES(X'). By subdividing sufficiently one can get arbitrarily fine control thus allowing one to map to a controlled version of the surgery exact sequence. This procedure is hoped to give rise to a 'controlled total surgery obstruction' analogous to Ranicki's algebraic total surgery obstruction.

## Teaching

During my three years of teaching Mathematics at the University of Glasgow I have lectured the following courses:

• 1R Calculus and Algebra,
• 1S Calculus and 1S Algebra,
• 2T: Topics in Discrete Maths,
• 5M: Advanced Differential Geometry and Topology,
• SMSTC Algebra 1 (lectures 6-7),
• SMSTC Geometry and Topology 1 (lectures 1-7 & 10).

I have also tutored the following courses:

• 1R and 1S,
• 2T: Topics in Discrete Maths,
• 3H & 3T: Analysis of Differentiation and Integration,
• 3H & 3R: Algebra,
• 3H: Metric Spaces and Basic Topology,
• 5M: Advanced Differential Geometry and Topology.

I have supervised the following undergraduate projects:

• 3H & 3W: Writing and presenting Mathematics projects on determinants of Vandermonde and Cauchy matrices,
• Level 4 projects on ``Calculus on Manifolds'' and ``Surgery on 3-Manifolds''.

I have been course head for 5M: Advanced Differential Geometry and Topology for the last three years and I have been course head for 2T: Topics in Discrete Maths for the last year.

## Publications and Preprints

### Preprints

• Triangular homotopy equivalences. (arXiv)
• A controlled local-global theorem for simplicial complexes. (arXiv)
• Algebraic subdivision in simplicially controlled categories. (arXiv)
• L-Homology on ball complexes and products. (arXiv)

### Other work

• Homeomorphisms, homotopy equivalences and chain complexes. PhD thesis, University of Edinburgh, 2012. (pdf)
• ## Contact details

If you wish to get in touch my work address, phone number and e-mail address are as below.