MAT 644 
Topics in Differential Geometry 
Fall 2019 

TΘ 1:00-2:20
Physics P-116

Prof. Claude LeBrun.
Office: Math Tower 3-108.
Office hours: TΘ 2:30--3:30 pm.

Mass, Scalar Curvature, and ALE Manifolds

Given a complete Riemannian manifold that looks enough like Euclidean space at infinity, physicists have defined a quantity called the mass that measures the asymptotic deviation of the geometry from the Euclidean model. This quantity is intimately related to the scalar curvature, and has played a a surprisingly role in the study of the scalar curvature of compact Riemannian manifolds. We will discuss the meaning and ramification of the mass in various settings, including that of ALE manifolds, where at infinity the space looks like a quotient of Euclidean space by a finite group of rotations.

Topics will include: proofs of the positive mass theorem, the role of mass in the Yamabe problem, breakdown of the positive mass theorem in the ALE setting, and special features of the Kähler case.

Grades will be based upon attendance and class participation.

The Professor may be reach by e-mail by .
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Illustration: The Schwarzschild wormhole.

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