Lough Swilly

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Seminars:

Mathematics Seminar

Irish Geometry Seminar

Suits you sir

Contact Details:

Martin Kerin
School of Mathematical and Statistical Sciences,
NUI Galway,
University Road,
Galway,
Ireland

email: martin.kerin AT nuigalway DOT ie
office: 218 Block S
phone: +353 91 49-2754

The main focus of my research is the geometry and topology of Riemannian manifolds with either non-negative or positive sectional curvature, often under an additional symmetry assumption. As the Bott Conjecture asserts that such manifolds are rationally elliptic, I am also interested in related questions in rational homotopy theory.

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Publications

  1. (with F. Galaz-García and M. Radeschi) Torus actions on rationally elliptic manifolds, Math. Z., to appear, PDF
  2. (with J. Harvey and K. Shankar) Semi-free actions with manifold orbit spaces, Documenta Math., to appear, PDF
  3. (with S. Goette and K. Shankar) Fake lens spaces and non-negative sectional curvature, Proceedings of the Australian-German Workshop on Differential Geometry in the Large, Cambridge Univ. Press, to appear, PDF
  4. (with S. Goette and K. Shankar) Highly connected 7-manifolds and non-negative sectional curvature, Ann. of Math. (2020), PDF
  5. (with S. Goette and K. Shankar) Non-negative curvature and the linking form, Oberwolfach Rep. (2018), Geometrie
  6. (with F. Galaz-García, M. Radeschi and M. Wiemeler) Torus orbifolds, slice-maximal torus actions and rational ellipticity, Int. Math. Res. Not. IMRN (2018) PDF
  7. (with S. Goette and K. Shankar) Non-negative sectional curvature on exotic 7-spheres, Oberwolfach Rep. (2016), Geometrie
  8. (with F. Galaz-García) Cohomogeneity-two torus actions on non-negatively curved manifolds of low dimension, Math. Z. (2014) PDF
  9. A note on totally geodesic embeddings of Eschenburg spaces into Bazaikin spaces, Ann. Glob. Anal. Geom. (2013) PDF
  10. (with K. Shankar) Riemannian submersions from simple, compact Lie groups, Münster J. of Math. (2012) PDF
  11. On the curvature of biquotients, Math. Ann. (2012) PDF
  12. Some new examples with almost positive curvature, Geom. Top. (2011) PDF
  13. (with J.-H. Eschenburg) Almost positive curvature on the Gromoll-Meyer sphere, Proc. Amer. Math. Soc. (2008) PDF
  14. (with D. Wraith) Homogeneous metrics on spheres, Irish Math. Soc. Bull. (2003) PDF

Preprints

  1. (with S. Goette and K. Shankar) Highly connected 7-manifolds, the linking form and non-negative sectional curvature, PDF
  2. (with J. DeVito and F. Galaz-García) Manifolds that admit a double disk-bundle decomposition, PDF

In preparation

  1. (with D. Corro and F. Galaz-García) Smooth 2-torus actions on the 5-sphere
  2. (with J. DeVito and F. Galaz-García) Obstructions to double disk-bundle decompositions

Lecture notes

Construction of manifolds with non-negative curvature: Biquotients. Lecture notes of a short course I taught at the summer school Téchnicas modernas en Geometría Riemanniana at UNAM, Mexico in 2014