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<p><b>新頁面</b></p><div>'''安德烈斯 ・ 洛爾'''（'''Andreas Floer'''，一九五六年八月二三—一九九一年五月十五 )，德國數學家，為幾何學、拓撲學以及數學物理等領域作出真可貴的開創性貢獻，並提出四配洛爾同調理論（Floer homology）， 一種誠實用的數學的工具。<br />
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==生平==<br />
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一九八二年波鴻魯大學數學系碩士，赴美國柏克萊加州大學深造，佇咧 Clifford Taubes 教授之指導之下攻讀博士學位，研究範圍為著「monopoles on 三-manifolds」，只因著愛回德服社會役，故無完成這个學業，尾仔佇一九八四年佇波鴻 Eduard Zehnder 教授之指導之下得著博士學位。<br />
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洛爾第一擺的關鍵貢獻，是解決若是干焦關於周拉基米 ・ 阿諾爾德 conjecture 佮 symplectomorphism 的問題。對阿諾爾德數學之研究佮家己所提出的同調理論（instanton homology）之成果，予洛爾深得世人之肯定，並且一九九空年八月到京都國際數學家大會發表演說。洛爾佇一九八九年領 Sloan Fellowship 獎學金。<br />
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佇一九八八年任柏克萊加州大學助理教授，佇咧一九九空年晉升做數學系正教授。對一九九空年起任波鴻魯大學數學教授，一直到雄雄一九九一年出人意料地自盡為止。<br />
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==評價==<br />
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" Andreas Floer's life was tragically interrupted , but his mathematical visions and striking contributions have provided powerful methods which are being applied to problems which seemed to be intractable only a few years ago . " [一]（安德烈斯 ・ 洛爾的生活雖然真不幸終止，但是伊對數學之遠見佮卓越貢獻，提供一寡真正是有效的方法，會當解決阮幾冬前閣當做無法度解決的問題。）<br />
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Simon Donaldson : " The concept of Floer homology is one of the most striking developments in differential geometry over the past 二十 years . . . . The ideas have led to great advances in the areas of low-dimensional topology and symplectic geometry and are intimately related to developments in Quantum Field Theory " [二] . . . " the full richness of Floer's theory is only beginning to be explored " . [三]（洛爾的同調理論這是二十冬以來微分幾何上上予人注目的發現之一…… 伊的創見佇幾若何拓撲學佮辛拓撲領域造成誠大的進步，閣有量的子場論是有啥物密切的關係。）……（阮目前才開始了解洛爾理論的規个價值。）<br />
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" Since its introduction by Andreas Floer in the late nineteen eighties , Floer theory has had a tremendous influence on many branches of mathematics including geometry , topology and dynamical systems . The development of new Floer theoretic tools continues at a remarkable pace and underlies many of the recent breakthroughs in these diverse fields . " [四]（自從安德烈斯 ・ 洛爾佇一九八空年代尾提出洛爾的理論，其實對數學真濟分支之影響真大，包括幾何、拓撲學佮動力系統。以洛爾的理論為基礎的新方法以足緊的速度繼續產生，袂少最近的突破攏是對伊出發的。）<br />
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==重要著作穡==<br />
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* Floer , Andreas . An instanton-invariant for 三-manifolds . Comm . Math . Phys . 一百十八葩 ( 一千九百八十八 ) , no . 二 , 兩百十五–兩百四十 . Project Euclid<br />
* Floer , Andreas . Morse theory for Lagrangian intersections . J . Differential Geom . 二十八 ( 一千九百八十八 ) , no . 三 , 五百一十三–五百四十七 .<br />
* Floer , Andreas . Cuplength estimates on Lagrangian intersections . Comm . Pure Appl . Math . 四十二 ( 一千九百八十九 ) , no . 四 , 三百三十五–三仔五十六 .<br />
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==參考文獻==<br />
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* Simon Donaldson , _ On the work of Andreas Floer _ , Jahresber . Deutsch . Math .-Verein . 九十五 ( 三 ) ( 一千九百九十三 ) , 一百空三石一百二十 .<br />
* The Floer Memorial Volume ( H . Hofer , C . Taubes , A . Weinstein , and E . Zehnder , eds . ) , Progress in Mathematics , vol . 一百三十三 , Birkhauser Verlag , 一千九百九十五 .<br />
* Simon Donaldson , _ Floer Homology Groups in Yang-Mills Theory _ , With the assistance of M . Furuta and D . Kotschick . Cambridge Tracts in Mathematics , 一百四十七喔 . Cambridge University Press , Cambridge , 兩千空二 . viii + 兩百三十六 pp . ISBN 空白五百二十一鋪八鋪空八百空三鋪空<br />
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==水產生出來的著作==<br />
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* Hofer , Helmut . Coherent orientation for periodic orbit problems in symplectic geometry ('''jointly with A . Floer''') Math . Zeit . 兩百十二 , 十三–三十八 , 一千九百九十三 .<br />
* Hofer , Helmut . Symplectic homology I : Open sets in C ^ n ('''jointly with A . Floer''') Math . Zeit . 兩百十五 , 三十七–八十八 , 一千九百九十四 .<br />
* Hofer , Helmut . Applications of symplectic homology I ('''jointly with A . Floer and K . Wysocki''') Math . Zeit . 兩百十七喔 , 五百七十七–六百空六 , 一千九百九十四 .<br />
* Hofer , Helmut . Symplectic homology II : A General Construction ('''jointly with K . Cieliebak and A . Floer''') Math . Zeit . 兩百十八 , 一百空三–一百二十二 , 一千九百九十五 .<br />
* Hofer , Helmut . Transversality results in the elliptic Morse theory of the action functional ('''jointly with A . Floer and D . Salamon''') Duke Mathematical Journal , Vol . 八十 No . 一 , 兩百五十一–兩百九十二 , 一千九百九十五 . Download from H . Hofer's homepage at NYU<br />
* Hofer , Helmut . Applications of symplectic homology II ('''jointly with K . Cieliebak , A . Floer and K . Wysocki''') Math . Zeit . 兩百二十三 , 二十七–四十五 , 九百九十六 .<br />
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==註解==<br />
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一 .'''^'''Hofer , Weinstein , and Zehnder , _ Andreas Floer : 一千九百五十六刣一千九百九十一 , _ Notices Amer . Math . Soc .'''三十八'''( 八 ) , 九百十一交九百十一二 .'''^'''Simon Donaldson , _ Floer Homology Groups in Yang-Mills Theory _ , With the assistance of M . Furuta and D . Kotschick . Cambridge Tracts in Mathematics , 一百四十七喔 . Cambridge University Press , Cambridge , 兩千空二 . viii + 兩百三十六 pp . ISBN 空白五百二十一鋪八鋪空八百空三鋪空 ( The above citation is from the front flap . )<br />
三 .'''^'''_ Mathematics : frontiers and perspectives _ . Edited by V . Arnold , M . Atiyah , P . Lax and B . Mazur . American Mathematical Society , Providence , RI , 兩千 . xii + 四仔五 pp . ISBN 空九八千二百一十八分二千空七十二 ( Amazon search )<br />
四 .'''^'''From the Press Release to the Workshop _ New Applications and Generalizations of Floer Theory _ of the Banff International Research Station ( BIRS ) , May 兩千空七 ( [五] )<br />
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==外部連結==<br />
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* 約翰 ・ J ・ 奧康納；埃德蒙 ・ F ・ 羅伯遴 , Floer , MacTutor 數學史檔案（英語）<br />
* The In Memoriam website of the Department of Mathematics at the University of California , Berkeley<br />
* The In Memoriam website of the University of California , Berkeley<br />
* Elaborate obituary by Addison / Casson / Weinstein at OAC , Online Archive of California , 一千九百九十二<br />
* 相片看 Wikimedia Commons Category : Andreas Floer 佮 a public Andreas Floer photo album on Facebook<br />
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