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Department of Mathematics pres.

Geometry Seminar

Recent developments in non-negative sectional curvature

In this talk we will present some recent progress in the study of non-negatively curved manifolds. We begin with a survey of some of the main theorems and obstructions in the least several decades as well as statements of some open problems and conjectures. This includes the seminal theorems of Gromov on the total Betti number, the Soul theorem of Cheeger and Gromoll for open manifolds as well as the Bott conjecture on the rational ellipticity of non-negatively curved manifolds. We then present results on recent progress in constructing non-negatively curved manifolds beginning with the work of Grove and Ziller in 2000. We conclude with a recent generalization of the Grove-Ziller construction as well as related results. Speaker(s): Krishnan Shankar (U Oklahoma/NSF)

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