I am a Lecturer in Mathematics at Maynooth University. Up until Summer 2017 I was an Associate Professor in Mathematics at Wichita State University, Kansas, USA. I completed my PhD at the University of Oregon at Eugene, under the supervision of Professor Boris Botvinnik, and spent time as a postdoctoral researcher at WWU Muenster, Germany, as well as Oregon State University in Corvallis. 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. More recently I have shifted my attention to analogous questions for positive Ricci curvature.
Papers:
1. Homotopy Groups of the Moduli Space of Metrics of Positive Scalar Curvature (co-authored with B. Botvinnik, B. Hanke and T. Schick), Geom. Topol. 14 (2010) 2047-2076. [29 pages]
2. Metrics of Positive Scalar Curvature and Generalised Morse Functions, Part 1, Mem. Amer. Math. Soc. 209 (2011), no. 983. [100 pages]
3. 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]
4. Metrics of Positive Scalar Curvature and Generalised Morse Functions, Part 2, Trans. Amer. Math. Soc. 366 (2014), no. 1, 1-50. [50 pages]
5. H-Spaces, Loop Spaces and Positive Scalar Curvature, Geom. Topol. 18 (2014), no. 4, 2189-2243. [55 pages]
6. Aspects of Scalar Curvature and Topology, Part 1, Bull. Irish Math. Soc. (2017) no. 80, 45-68. [24 pages]
7. Aspects of Scalar Curvature and Topology, Part 2, Bull. Irish Math. Soc. (2018) no. 81, 57-95. [38 pages]
8. The Observer Moduli Space of Metrics of Positive Ricci Curvature (co-authored with B. Botvinnik and D. Wraith), Geom. Topol. 23 (2019), 3003-3040. [38 pages]
9. The Space of Positive Scalar Curvature Metrics on a Manifold with Boundary, New York J. Math. Vol. 26 (2020), 853-930. [78 pages]
10. Homotopy Invariance of the Space of Metrics with Positive Scalar Curvature on Manifolds with Singularities (co-authored with B. Botvinnik), SIGMA 17 (2021), 034, Special Issue on Scalar and Ricci Curvature in honor of Misha Gromov on his 75th Birthday [27 pages]
11. H-Space and Loop Space Structures for Intermediate Ricci Curvatures (co-authored with D. Wraith), To appear in Communications in Contemporary Mathematics (2022), Preprint at https://arxiv.org/abs/2008.12045 [37 pages]
12. Positive p-Curvature Metrics and Gromov-Lawson Cobordism (co-authored with Matthew Burkemper and Catherine Searle), To appear in Journal of Geometry and Physics (2022), Preprint at https://arxiv.org/pdf/2110.12069.pdf [32 pages]
Stuff I care about:
Jeff Weeks' Geometry and Topology Website
My Father's Book: The Great Calendar Reform ---------->
Useful Mathematical Links:
Mathematical Association of America
A local geometrical wonder: The Wonderful Barn in Leixlip
