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I am 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

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
 
3. Metrics of Positive Scalar Curvature and Generalised Morse Functions, Part 2
    Trans. Amer. Math. Soc. 366 (2014), no. 1, 1-50.

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.

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

6. The Space of Positive Scalar Curvature Metrics on a Manifold with Boundary
    Submitted to Geom. Top, Preprint on arxiv.org

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

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