| Prof. Richard S. Palais
(
Brandeis University /國家理論科學中心訪問學者 )
The Magic of Symmetry.
摘要
| | 1. 附註：各週五下午，共八次演講。
2. 對象：數學系及理工學院大學部學生、研究生，以及數理學者等。
3. 簡介：本系列演講是在介紹數學與物理上“對稱性”的有用性。就給定之數學或物理模型來瞭解其對稱性，不僅可以簡化若干求此模型方程式的解的過程，有時亦可建立該模型方程式為何種形式。我們將學習對稱性的一般技巧，並且應用到一些特定的模型上，包括古典質點力學、特殊、廣義相對論以及其他等。
4. 綱要：
(1) Overview: The uses of symmetry in mathematics and physics. Not only can an undersanding of the symmetries of a given mathematical or physical model simplify the process of finding solutions to the model equations, but also they can sometimes even determine what the form of the equations must be. We are going to look at some general techniques for using symmetry and apply these ideas to a number of specific models from classical particle mechanics to Special and General Relativity and beyond.
(2) Symmetry Principles in Lagrangian and Hamiltonian Mechanics. Noethers Principle.
(3) From Gallilean Invariance to Newton's Laws of Motion.
(4) The Symmetric Criticality Principle: Justifying and Understanding the Technique of using a Symmetry Ansatz to reduce a PDE to an ODE.
(5) Lorentz Invariance and Special Relativity.
(6) Diffeomorphism Invariance and General Relativity.
(7) Gauge Invariance and Kaluza-Klein Theories. |
91年1月11日 (星期五)
15:10-16:10;16:30-17:30
台灣大學數學系新數館103室
附註：地點更改至新數館103室
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