Week 1 1 May 2025 | Introduction and overview
Speaker: Jason Lotay
Abstract: This talk will introduce Einstein manifolds, describe the fundamental open questions and give an overview of the advanced class. [Jason's handwritten notes]
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Week 2 8 May 2025 | Homogeneous Einstein manifolds
Speaker: Andrew Dancer
Abstract: This talk will survey the state-of-the-art in the study of homogeneous Einstein metrics, focussing on existence questions in the compact setting. [Andrew's handwritten notes]
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Week 3 15 May 2025 | Cohomogeneity one Einstein manifolds
Speaker: Andrew Dancer
Abstract: The cohomoeneity one technique has proven to effective in various geometric problems, including the study of Einstein metrics. This talk will explain the method then describe some of its various applications and success, including in 4 dimensions and in the construction of exotic Einstein metrics on spheres. [Andrew's handwritten notes] |
Week 4 22 May 2025 | New cohomogeneity one Einstein manifolds and numerical methods
Speaker: Qiu Shi Wang
This talk will discuss the recent work of Buttsworth-Hodgkinson concerning Einstein metrics on the 12-sphere which combines cohomogeneity one techniques with numerical approximation. Potentially, follow-up work by the speaker will also be described. [Qiu Shi's handwritten notes]
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Week 5 29 May 2025 | Ricci flow in dimension 4 and orbifold singularities (Part 1)
Speaker: John Hughes
These talks will give an overview of work by Deruelle-Ozuch relating Ricci flow in dimension 4 to orbifold singularities and Ricci-flat ALE metrics. [John's handwritten notes]
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Week 6 5 June 2025 | Ricci flow in dimension 4 and orbifold singularities (Part 2)
Speaker: John Hughes
These talks will give an overview of work by Deruelle-Ozuch relating Ricci flow in dimension 4 to orbifold singularities and Ricci-flat ALE metrics.
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Week 7 12 June 2025 | Construction of non-locally symmetric Einstein manifolds
with negative curvature (Part 1)
Speaker: Thibault Langlais
These talks will describe the work of Hamenstädt-Jäckel constructing infinitely many new Einstein n-manifolds for each n at least 4 which have negative scalar curvature. [Thibault's notes]
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Week 8 19 June 2025 | Construction of non-locally symmetric Einstein manifolds
with negative curvature (Part 2)
Speaker: Thibault Langlais
These talks will describe the work of Hamenstädt-Jäckel constructing infinitely many new Einstein n-manifolds for each n at least 4 which have negative scalar curvature. [Thibault's notes]
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