Differential Geometry and Topology

course: Q-curvature in conformal geometry

speaker: Sun-Yung (Alice) Chang (Princeton University)

abstract: Gaussian curvature and scalar curvatures play an important role in the study of the geometry of surfaces and manifolds of dimension greater than 2. In recent years, some polynomials formed by the contraction of curvatures and their derivatives called the Q-curvature play a crucial role in the study of conformal invariants and other problems in conformal geometry. I shall describe some of the recent developments in the subject. More precisely, starting from the construction method of C. Fefferman and R. Graham, I will discuss the work of R. Graham and Zworski relating the subject to singularities of the scattering matrix on conformally compact Einstein manifolds, and among others, recent work of Chang, J. Qing and P. Yang relating Q-curvature to the renormalized volume of conformally compact Einstein manifolds. I will also discuss some PDE aspects of Q-curvature.

The first talk (Friday Week 7) is likely to be a survey, the second (Monday Week 8) will cover my recent work.

timetable:
Fri 22 Oct, 15:30 - 17:00, Sala Conferenze Centro De Giorgi
Mon 25 Oct, 17:00 - 18:15, Sala Conferenze Centro De Giorgi
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