The Noether Theorems in Geometry:
Then and Now
幾何學中的諾特定理：過去與現在
Speaker / 主講人
Karen Uhlenbeck （Institute for Advanced Study）
Time / 時間
2021。12。9 | 9：30 am ET
2021年 12 月 9 日 北京時間 22:30
Abstract
The 1918 Noether theorems were a product of the general search for energy and momentum conservation in Einstein’s newly formulated theory of general relativity。 Although widely referred to as the connection between symmetry and conservation laws， the theorems themselves are often not understood properly and hence have not been as widely used as they might be。 In the first part of the talk， I outline a brief history of the theorems， explain a bit of the language， translate the first theorem into coordinate invariant language and give a few examples。 I will mention only briefly their importance in physics and integrable systems。 In the second part of the talk， I describe why they are still relevant in geometric analysis： how they underlie standard techniques and why George Daskalopoulos and I came to be interested in them for our investigation into the best Lipschitz maps of Bill Thurston。 Some applications to integrals on a domain a hyperbolic surface leave open possibilities for applications to integrals on domains which are locally symmetric spaces of higher dimension。 The talk finishes with an example or two from the literature。
Speaker
Karen Keskulla Uhlenbeck （born August 24， 1942） is an American mathematician and one of the founders of modern geometric analysis。 She is a professor emeritus of mathematics at the University of Texas at Austin， where she held the Sid W。 Richardson Foundation Regents Chair。 She is currently a Distinguished Visiting Professor at the Institute for Advanced Study and a visiting senior research scholar at Princeton University。
Uhlenbeck was elected to the American Philosophical Society in 2007。 She won the 2019 Abel Prize for “her pioneering achievements in geometric partial differential equations， gauge theory， and integrable systems， and for the fundamental impact of her work on analysis， geometry and mathematical physics。” She is the first， and so far only， woman to win the prize since its inception in 2003。 She donated half of the prize money to organizations which promote more engagement of women in research mathematics。
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