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I am a Lecturer in Mathematics at Maynooth University. Up until Summer 2017 I was an Associate Professor in Mathematics at Wichita State University. My interests are in Geometry, in particular the relationship between Curvature and Topology. My work so far has focused on Positive Scalar Curvature and especially understanding the topology of the space of Riemannian metrics of positive scalar curvature on a smooth manifold.


Papers:

1. Metrics of Positive Scalar Curvature and Generalised Morse Functions, Part 1
    Memoirs of the AMS 209 (2011), no. 983. [100 pages]

2. Homotopy Groups of the Moduli Space of Metrics of Positive Scalar Curvature
    (co-authored with B. Botvinnik, B. Hanke and T. Schick)
    Geometry and Topology 14 (2010) 2047-2076. [29 pages]
 
3. Metrics of Positive Scalar Curvature and Generalised Morse Functions, Part 2
    Trans. Amer. Math. Soc. 366 (2014), no. 1, 1-50. [50 pages]

4. Cobordism Invariance of the Homotopy Type of the Space of Positive Scalar Curvature Metrics
    Proc. Amer. Math. Soc. 141 (2013), no. 7, 2475-2484. [10 pages]

5. H-Spaces, Loop Spaces and Positive Scalar Curvature
    Geometry and Topology 18 (2014), no. 4, 2189-2243. [55 pages]

6. The Observer Moduli Space of Metrics of Positive Ricci Curvature 
    Preprint on arxiv.org. [28 pages]

7. The Space of Positive Scalar Curvature Metrics on a Manifold with Boundary
    Submitted, Preprint on arxiv.org. [77 pages]

8. Aspects of Scalar Curvature and Topology 
     Survey article to appear in Bulletin of the Irish Mathematical Society, [60 pages]

9. Cobordism Categories and the Gromov-Lawson Construction
    joint work with B. Botvinnik 
    in preparation

10. The Moduli Space of Metrics of Positive Ricci Curvature
     joint with B. Botvinnik and D. Wraith
    in preparation

11. Preserving Isotopy Type under Surgery on Metrics of Positive Scalar Curvature
    in preparation



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