Primary Title:

Visiting Professor

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PhD in Mathematics, University of Oregon, 2009

MSc in Mathematics, NUI Maynooth, 2002

Higher Diploma (First Class Honours), NUI Maynooth, 2000

Research Field:

Riemannian Geometry, Algebraic Topology, Differential Topology

Research Description:

Mark Walsh's research deals with the relationship between curvature and topology on smooth manifolds. This is a rich subject combining techniques from Geometry, Topology and Analysis. In particular, Walsh is interested in metrics of positive scalar curvature (psc-metrics). Although the problem of whether or not a particular smooth manifold admits a psc-metric has been studied extensively, relatively little is known about the topology of the space of psc-metrics on a given manifold, or it's corresponding moduli spaces. Much of Walsh's work involves the creation of tools for constructing interesting families of psc-metrics. This has helped show, for example, the non-triviality of certain higher homotopy groups of the moduli space of psc-metrics.

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