現代数学の系譜11 ガロア理論を読む9at MATH現代数学の系譜11 ガロア理論を読む9 - 暇つぶし2ch■コピペモード□スレを通常表示□オプションモード□このｽﾚｯﾄﾞのURL■項目テキスト20:１３２人目の素数さん 14/08/17 17:48:39.76 >>9 関連 >【2014年フィールズ賞発表】イラン出身のスタンフォード大教授、女性として初めて受賞 >プリンストン高等研究所教授の理論物理学者エドワード・ウィッテンの推測を証明したことが高く評価された。 http://en.wikipedia.org/wiki/Maryam_Mirzakhani 17 Mirzakhani, Maryam (2008). "Growth of the number of simple closed geodesics on hyperbolic surfaces". Annals of Mathematics 168 (1): 97–125. doi:10.4007/annals.2008.168.97. MR 2415399. Zbl 1177.37036. 論文PDF http://annals.math.princeton.edu/wp-content/uploads/annals-v168-n1-p03.pdf Growth of the number of simple closed geodesics on hyperbolic surfaces Annals of Mathematics, 168 (2008), 97–125 21:１３２人目の素数さん 14/08/17 18:18:11.33 >>20 関連 http://www.mathunion.org/fileadmin/IMU/Prizes/2014/news_release_mirzakhani.pdf The Work of Maryam Mirzakhani - International Mathematical Union 抜粋 Riemann knew that these deformations depend on 6g - 6 parameters or "moduli", meaning that the "moduli space" of Riemann surfaces of genus g has dimension 6g - 6. However, this says nothing about the global structure of moduli space, which is extremely complicated and still very mysterious. Moduli space has a very intricate geometry of its own, and dierent ways of looking at Riemann surfaces lead to dierent insights into its geometry and structure. For example, thinking of Riemann surfaces as algebraic curves leads to the conclusion that moduli space itself is an algebraic object called an algebraic variety. In Mirzakhani's proof of her counting result for simple closed geodesics, another structure on moduli space enters, a so-called symplectic structure, which, in particular, allows one to measure volumes (though not lengths). Generalizing earlier work of G. McShane, Mirzakhani establishes a link between the volume calculations on moduli space and the counting problem for simple closed geodesics on a single surface. She calculates certain volumes in moduli space and then deduces the counting result for simple closed geodesics from this calculation. つづく 次ページ最新レス表示レスジャンプ類似スレ一覧スレッドの検索話題のニュースおまかせリストオプションしおりを挟むスレッドに書込スレッドの一覧暇つぶし2ch