Guoyi Xu
In the first part of my talk I will try to explain the correspondence between physical concepts occurring in general relativity and well-known mathematical objects. In particular will explain how the physical concepts of observers, free falling particles, reference frames, space-time, energy, etc., are related to the mathematical notions of curves, vector fields, 4-dimensional manifolds, functions defined on curves, etc.. In the second part of the talk I will describe Newton's equations by elliptic PDE, introduce Maxwell's equations, and then discuss the famous Einstein equations G=T+E. I will in particular explain the hyperbolic essence of Einstein equations.
Throughout the talk I will try to highlight the importance of differential geometry and other mathematical subjects. The motivation will be taken from general relativity.
No knowledge in physics is required, the talk will focus on the mathematical concepts originating from general relativity. Only basic knowledge in differential geometry and analysis will be assumed.
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