Room 505, Cosmology Building, National Taiwan University + Cisco WebEx, Physical+Online Seminar
(實體+線上演講 台灣大學次震宇宙館505研討室+ Cisco WebEx)
Conformal Circles, Local Diffeomorphisms, and Their Holographic Interpretation
Tzu-Mo Kuo (University of California, Santa Cruz)
Abstract
In the context of a pseudo-Riemannian conformal manifold
![](https://chart.googleapis.com/chart?cht=tx&chl=%24(M%5En%2C%20%5Bg%5D)%24%20&chf=bg,s,333333&chco=ffffff)
with
![](https://chart.googleapis.com/chart?cht=tx&chl=%24n%20%5Cgeq%202%24&chf=bg,s,333333&chco=ffffff)
, a distinguished family of curves known as conformal circles, or conformal geodesics, emerges. These curves satisfy a third-order differential equation for non-null conformal circles. One classical problem is to determine whether conformal circles are essential for a conformal manifold by considering whether a diffeomorphism is a conformal diffeomorphism, provided it maps unparametrized conformal circles to unparametrized conformal circles. In this presentation, I will introduce the definition of a conformal circle and discuss its holographic interpretation. Additionally, I will present my results concerning both the classical problem and the holographic interpretation of the problem.
Meeting number (access code): 2514 033 9066
Meeting password: daS58yYr6Ja
Organizers: Nicolau Sarquis Aiex (NTNU), Siao-Hao Guo (NTU), Ulrich Menne (NTNU), Chung-Jun Tsai (NTU)