演講公告
新聞標題: ( 2023-11-24 )
演講主題:Conformal Geometry on 4-manifolds
主講人:張聖容教授(普林斯頓大學數學系)
演講日期:2023年12月15日(五) 11:00 - 12:00
演講地點:(光復校區) 科學一館223室
摘要內容:
In this talk, I will give a survey talk on results and PDE techniques in conformal geometry.
On 4-manifolds, one of the key ingredients is the study of the integrand of the Chern-
Gauss-Bonnet formula. The part that involves the Ricci tensor gives a fully non-linear PDE
known as the second elementary symmetric equation. It turns out this PDE can be studied
via a 4-th order linear operator (part of the family of GJMS operator) and its associated 4-th
order curvature called the Q-curvature. I will explain the connection and give an application
of using this concept to compute the renormalized volume.
As another application, we will study the problem of ”conformal filling in” in ADS/CFT
theory. Namely, given a manifold (Mn; [h]), when is it the boundary of a conformally compact
Einstein manifold ( Xn+1; g+) with r2
g+|M = h for some defining function r on Xn+1?
The model example is the n-sphere as the conformal infinity of the hyperbolic (n+1) ball.相關檔案:Talk_20231215.pdf