{"id":1592,"date":"2012-03-26T22:21:45","date_gmt":"2012-03-26T14:21:45","guid":{"rendered":"http:\/\/vanabel.sinaapp.com\/?p=1592"},"modified":"2012-03-26T22:21:45","modified_gmt":"2012-03-26T14:21:45","slug":"%e6%9c%89%e6%9c%8b%e8%87%aa%e9%81%a0%e6%96%b9%e4%be%86%e4%b8%80%e4%b8%80%e5%b0%88%e8%a8%aa%e6%b7%b1%e8%b0%b7%e8%b3%a2%e6%b2%bb","status":"publish","type":"post","link":"https:\/\/lttt.vanabel.cn\/?p=1592","title":{"rendered":"\u6709\u670b\u81ea\u9060\u65b9\u4f86\u4e00\u4e00\u5c08\u8a2a\u6df1\u8c37\u8ce2\u6cbb"},"content":{"rendered":"

Kenjin Fukaya<\/a>
\n\"\"<\/a><\/p>\n

\u6709\u670b\u81ea\u8fdc\u65b9\u6765\u4e00\u4e00\u4e13\u8bbf\u6df1\u8c37<\/h1>\n

\u8d24\u6cbb (Kenji Fukaya)\u6559\u6388<\/h1>\n

\u7b56\u5212 :\u5218\u592a\u5e73<\/p>\n

\u8bbf\u95ee :\u5218\u592a\u5e73\u3001\u90d1\u65e5\u65b0\u3001\u6c5f\u5b5f\u84c9\u65f6\u95f4 :\u6c11\u56fd98\u5e74 5\u670810\u65e5\u5730\u70b9 :\u4e2d\u592e\u7814\u7a76\u9662\u6570\u5b66\u6240<\/p>\n

\u6574\u7406 :\u9648\u4e3d\u4f0d<\/p>\n

 <\/p>\n

 <\/p>\n

\u6df1\u8c37\u8d24\u6cbb (Kenji Fukaya)\u6559\u6388\u751f\u4e8e\u516c\u51431959\u5e74, 1978\u5e74\u8fdb\u4e1c\u4eac\u5927\u5b66 ,\u4e00\u8def\u5230 1986\u5e74\u5f97\u535a\u58eb\u5b66\u4f4d\u3002\u521d\u4e8e\u4e1c\u4eac\u5927\u5b66\u4efb\u804c\u81f3\u526f\u6559\u6388, 1994\u5e74\u8f6c\u4efb\u4eac\u90fd\u5927\u5b66\u6559\u6388\u3002\u4e13\u4e1a\u51e0\u4f55,\u7279\u522b\u662f\u8f9b\u51e0\u4f55\u3002\u65e9\u671f\u505a\u9ece\u66fc\u6d41\u5f62\u7684\u5d29\u584c (collapsing)\u95ee\u9898,\u66fe\u4e0e Cheeger, Gro\u00admov\u5408\u4f5c\u3002\u5728\u51e0\u4e4e\u975e\u8d1f\u6d41\u5f62\u7684\u57fa\u672c\u7fa4\u7814\u7a76\u4e0a\u4e0eT. Yamaguchi\u5408\u4f5c ,\u4e5d\u96f6\u5e74\u521d\u671f\u8f6c\u5165\u8f9b\u51e0\u4f55,\u56e0 Floer\u5de5\u4f5c\u7684\u542f\u53d1,\u5f00\u59cb\u53d1\u5c55\u540e\u6765\u6240\u8c13\u7684 Lagrangian intersection Floer\u7406\u8bba (FOOO\u7406\u8bba),\u8054\u5408\u4e09\u201cO\u201d\u5373 Oh, Ohta, Ono,\u5b9a\u4e49\u4e86\u76f8\u5173\u7684 Floer\u540c\u8c03,\u63a8\u5e7f\u4e86\u539f Arnold\u731c\u60f3\u7684\u89c6\u91ce,\u53d1\u73b0 A\u221e<\/sup>\u4ee3\u6570\u7684\u7ed3\u6784,\u5065\u5168\u4e86 Kontsevich\u540c\u8c03\u955c\u5bf9\u79f0 (homological mirror symmetry)\u4e2d\u5173\u4e8e\u8f9b\u51e0\u4f55\u65b9\u9762\u7684\u63cf\u8ff0\u3002\u6df1\u8c37\u624d\u601d\u654f\u9510,\u683c\u5c40\u5b8f\u5927,\u66fe\u83b7\u65e5\u672c\u5404\u79cd\u5956\u8d4f,\u662f\u65e5\u672c\u8fd1\u5e74\u6765\u96be\u5f97\u7684\u5fae\u5206\u51e0\u4f55\u9886\u5bfc\u4eba\u7269\u3002<\/em><\/p>\n

 <\/p>\n

\u5218\u592a\u5e73(\u4ee5\u4e0b\u7b80\u79f0\u300c\u5218\u300d):\u597d,\u6211\u4eec\u5f00\u59cb\u5427\u3002\u9996\u5148\u8981\u8c22\u8c22\u4f60\u62bd\u51fa\u65f6\u95f4\u63a5\u53d7\u6211\u4eec\u7684\u8bbf\u95ee,\u6211\u4eec\u5e0c\u671b\u53ef\u4ee5\u85c9\u6b64\u673a\u4f1a\u542c\u542c\u4f60\u7684\u60f3\u6cd5\u3002\u90d1\u65e5\u65b0\u6559\u6388\u7279\u522b\u51c6\u5907\u4e86\u4e00\u4e9b\u5178\u578b\u7684\u95ee\u9898,\u5c31\u8ba9\u6211\u4ece\u4e0b\u9762\u8fd9\u4e2a\u5178\u578b\u7684\u95ee\u9898\u5f00\u59cb:\u300e\u4f60\u5982\u4f55\u5bf9\u6570\u5b66\u53d1\u751f\u5174\u8da3?\u300f<\/p>\n

\u6df1\u8c37\u8d24\u6cbb (\u4ee5\u4e0b\u7b80\u79f0\u300c\u6df1\u8c37\u300d):\u6211\u5148\u8bf4\u660e\u5927\u90e8\u5206\u7684\u6570\u5b66\u5bb6\u4e0d\u592a\u5584\u4e8e\u4e0e\u4eba\u4ea4\u8c08,\u6bd4\u8f83\u5185\u5411 ,\u6211\u5c31\u662f\u5982\u6b64\u3002\u6570\u5b66\u7684\u597d\u5904\u662f\u4f60\u4e0d\u9700\u8981\u7275\u626f\u5230\u4efb\u4f55\u653f\u6cbb ,\u6570\u5b66\u91cc\u5bf9\u7684\u5c31\u662f\u5bf9\u7684,\u4e0d\u9700\u8981\u8c08\u5224\u4ea4\u6d89,\u8fd9\u5bf9\u4e8e\u50cf\u6211\u8fd9\u6837\u7684\u4eba\u800c\u8a00\u662f\u4ef6\u597d\u4e8b\u3002<\/p>\n

<\/p>\n

\u90d1\u65e5\u65b0 (\u4ee5\u4e0b\u7b80\u79f0\u300c\u90d1\u300d):\u4f60\u4ec0\u4e48\u65f6\u5019\u559c\u6b22\u4e0a\u6570\u5b66\u7684?\u9ad8\u4e2d?<\/p>\n

\u6df1\u8c37:\u55ef,\u9ad8\u4e2d,\u6211\u8bfb\u4e86\u4e9b\u5927\u5b66\u7528\u4e66 ,\u4e0d\u8fc7\u4e24\u8005\u4e4b\u95f4\u6beb\u65e0\u5173\u8054\u3002<\/p>\n

\u90d1:\u4f60\u9ad8\u4e2d\u5c31\u51b3\u5b9a\u8981\u4ece\u4e8b\u6570\u5b66\u8fd9\u65b9\u9762\u7684\u5de5\u4f5c\u5417?<\/p>\n

\u6df1\u8c37:\u6ca1\u9519\u3002\u6211\u5728\u9ad8\u4e2d\u5373\u5c06\u6bd5\u4e1a\u8fdb\u5165\u5927\u5b66\u4e4b\u524d ,\u5f00\u59cb\u5f88\u8ba4\u771f\u7684\u601d\u8003\u8fd9\u4ef6\u4e8b\u60c5\u3002\u5728\u9ad8\u4e09\u7684\u65f6\u5019\u5c31\u5df2\u7ecf\u51c6\u5907\u8981\u5ff5\u6570\u5b66\u4e86\u3002<\/p>\n

\u90d1:\u6240\u4ee5\u4f60\u8fdb\u4e1c\u4eac\u5927\u5b66\u4e3b\u4fee\u6570\u5b66 ?<\/p>\n

\u6df1\u8c37:\u662f\u7684 ,\u4e1c\u4eac\u5927\u5b66\u662f\u7b2c\u4e09\u5e74\u624d\u5206\u79d1\u7cfb,\u5934\u4e24\u5e74\u4e0d\u9700\u8981\u51b3\u5b9a\u4e3b\u4fee ,\u4e0d\u8fc7\u6211\u5728\u7b2c\u4e00\u5e74\u5c31\u786e\u5b9a\u8981\u5ff5\u6570\u5b66\u4e86\u3002<\/p>\n

\u5218:\u90a3\u65f6\u5728\u65e5\u672c ,\u4f60\u4eec\u9ad8\u4e2d\u5c31\u5f00\u59cb\u5b66\u4e00\u4e9b\u6bd4\u8f83\u6df1\u5165\u7684\u6570\u5b66\u50cf\u5fae\u79ef\u5206,\u662f\u5417?<\/p>\n

\u6df1\u8c37:\u662f\u7684 ,\u9ad8\u4e2d\u91cc\u662f\u6559\u4e86\u4e9b\u5fae\u79ef\u5206,\u4e0d\u8fc7\u6211\u81ea\u4fee\u4e86\u4e00\u4e9b\u6570\u5b66\u7684\u4e66\u3002<\/p>\n

\u5218:\u539f\u6765\u5982\u6b64,\u54ea\u4e9b\u4e66\u5462?<\/p>\n

\u6df1\u8c37:\u6211\u4e0d\u592a\u63a8\u8350\u8fd9\u4e9b\u4e66,\u6211\u8bfb\u4e86 S. Lang1<\/sup>\u5173\u4e8e\u5206\u6790\u7684\u4e66\u3002\u9ad8\u4e2d\u6700\u540e\u4e00\u5e74,\u6211\u5ff5\u4e86 F. Riesz\u548c B. Sz. Nagy\u5408\u5199\u7684\u6cdb\u51fd\u5206\u67902 <\/sup>, \u8fd9\u672c\u4e66\u6211\u5f88\u559c\u6b22\u3002<\/p>\n

\u5218: Riesz-Nagy\u7684\u6cdb\u51fd\u5206\u6790?\u4f60\u9ad8\u4e2d\u5c31\u5ff5\u4e86\u8fd9\u672c\u4e66 ?!<\/p>\n

\u6df1\u8c37:\u662f\u7684 ,\u9ad8\u4e09\u5ff5\u7684\u3002\u9ad8\u4e8c\u65f6\u6211\u5ff5\u7684\u662f\u4fc4\u56fd\u4eba\u5199\u7684\u5fae\u79ef\u5206\u4e00\u7c7b\u7684\u4e66 ,\u5f53\u7136\u662f\u7ffb\u8bd1\u6210\u65e5\u6587\u7684 ,\u4e66\u540d\u3001\u4f5c\u8005\u90fd\u4e0d\u8bb0\u5f97\u4e86,\u8fd9\u662f\u6211\u559c\u6b22\u7684 ,\u6bd4\u8f83\u4ee5\u5e94\u7528\u4e3a\u5bfc\u5411\u7684\u4e66\u3002<\/p>\n

\u5218:\u6709\u4e00\u672c\u9ad8\u6728\u8d1e\u6cbb (Teiji Takagi)\u7684\u4e66 3 <\/sup>,\u5728\u65e5\u672c\u5f88\u6709\u540d,\u4f7f\u7528\u7684\u4eba\u5f88\u591a\u3002<\/p>\n

\u6df1\u8c37:\u662f\u7684 ,\u662f\u8fd9\u6837,\u4e0d\u8fc7\u6211\u4ece\u6ca1\u5ff5\u8fc7\u9ad8\u6728\u5fae\u79ef\u5206\u7684\u4e66\u3002\u6211\u81ea\u5df1\u4e5f\u89c9\u5f97\u5947\u602a\u4e3a\u4ec0\u4e48\u6211\u6ca1\u5ff5\u8fc7\u3002\u65e5\u672c\u5927\u5b66\u5165\u5b66\u8003\u8bd5\u76f8\u5f53\u56f0\u96be,\u4e3a\u4e86\u51c6\u5907\u8003\u8bd5 ,\u8003\u524d\u4e0d\u80fd\u968f\u5fc3\u6240\u6b32\u7684\u5b66\u4e60,\u5ff5\u81ea\u5df1\u60f3\u5ff5\u7684\u4e66\u3002\u901a\u8fc7\u5165\u5b66\u8003\u8bd5\u540e,\u6211\u60f3\u5ff5\u4e00\u4e9b\u6570\u5b66\u4e66,\u5c31\u5ff5\u4e86\u4e24\u672c-vanderWaerden\u7684\u4ee3\u65704<\/sup>\u4e0e\u4e00\u672c\u62d3\u6734\u7684\u4e66\u3002\u6211\u4e5f\u4e0d\u77e5\u9053\u4e3a\u4ec0\u4e48\u4f1a\u9009\u62e9 John Kelley5<\/sup>\u7684\u62d3\u6734\u3002\u90a3\u65f6\u5019\u62d3\u6734\u7684\u4e66\u975e\u5e38\u5438\u5f15\u6211,\u4e5f\u8bb8\u56e0\u4e3a\u5f53\u65f6\u6211\u5f88\u5e74\u8f7b\u3002\u51e0\u5e74\u540e ,\u6211\u8f6c\u79fb\u5174\u8da3,\u4e0d\u8fc7\u73b0\u5728\u53c8\u89c9\u5f97\u62d3\u6734\u8fd8\u662f\u6ee1\u6709\u610f\u601d\u7684\u3002<\/p>\n

\u90d1:\u8fdb\u5927\u5b66\u540e,\u9664\u4e86\u6570\u5b66\u662f\u4e0d\u662f\u8fd8\u6709\u5176\u4ed6\u611f\u5174\u8da3\u7684\u79d1\u76ee?<\/p>\n

\u6df1\u8c37:\u6211\u66f4\u5e74\u8f7b\u7684\u65f6\u5019,\u5bf9\u5929\u6587\u6709\u5174\u8da3\u3002\u4f46\u662f\u5f88\u5feb\u7684\u5c31\u77e5\u9053\u81ea\u5df1\u8fd9\u65b9\u9762\u4e0d\u884c\u3002\u66fe\u7ecf\u52a0\u5165\u4e00\u4e2a\u5929\u6587\u7684\u793e\u56e2,\u4e0a\u5c71\u53bb\u770b\u661f\u661f\u65f6\u522b\u4eba\u77e5\u9053\u5982\u4f55\u8c03\u6574\u671b\u8fdc\u955c\u3001\u955c\u5934\u7b49\u7b49 ,\u6211\u5219\u4e0d\u7136,\u90a3\u65f6\u5c31\u51b3\u5b9a\u8fd9\u4e0d\u662f\u6211\u80fd\u505a\u7684\u4e8b\u3002<\/p>\n

\u5218:\u4e0a\u9762\u63d0\u5230\u7684\u4e66 ,\u4f60\u662f\u548c\u5176\u4ed6\u670b\u53cb\u4e00\u8d77\u5ff5,\u8fd8\u662f\u4e00\u4e2a\u4eba\u5ff5\u7684 ?\u4f60\u53c8\u662f\u600e\u4e48\u77e5\u9053\u8fd9\u4e9b\u4e66\u7684 ?<\/p>\n

1<\/sup>\u8bd1\u6ce8 :\u6307 Serge Lang(1927-2005),\u56e0\u4ed6\u5728\u4ee3\u6570\u7684\u5de5\u4f5c\u548c\u7f16\u5199\u7684\u591a\u672c\u6559\u79d1\u4e66\u800c\u95fb\u540d\u3002\u4ed6\u7684\u6559\u79d1\u4e66\u5b9a\u4f4d\u4e8e\u7eaf\u6570\u5b66,\u4ee5\u4e60\u9898\u539f\u521b\u95fb\u540d\u3002<\/p>\n

2<\/sup>\u8bd1\u6ce8 : Frigyes Riesz and B\u00b4ela Sz\u00a8okefalvi Nagy, Le\u00b8cons d\u2019analyse fonctionnelle. <\/p>\n

3<\/sup>\u8bd1\u6ce8 :\u6307\u9ad8\u6728\u8d1e\u6cbb (Teiji Takagi, 1875-1960),\u4e3b\u8981\u8d21\u732e\u5728\u4ee3\u6570\u5b66\u8bba\u65b9\u9762\u3002\u5199\u4e86\u8bb8\u591a\u5927\u5b66\u6559\u6750\u3001\u4e2d\u5c0f\u5b66\u6559\u79d1\u4e66\u53ca\u5404\u79cd\u666e\u53ca\u8bfb\u7269\u3002\u5173\u4e8e\u9ad8\u6728\u6559\u6388\u4e4b\u751f\u5e73\u4e8b\u8ff9,\u8be6\u89c1\u6570\u5b66\u4f20\u64ad\u7b2c 23\u5377,\u7b2c 2, 3\u671f\u3002 <\/p>\n

4<\/sup>\u8bd1\u6ce8 : B. L. van der Waerden, Algebra I, Springer-Verlag, 1991, ISBN 0-387-97424. <\/p>\n

5<\/sup>\u8bd1\u6ce8 : John L. Kelley, General Topology, Springer-Verlag, 1955, ISBN 0-387-90125-6.<\/p>\n

<\/p>\n

\u6df1\u8c37:\u4e8b\u5b9e\u4e0a ,\u9ad8\u4e2d\u65f6\u6211\u6700\u7231\u505a\u7684\u4e8b\u5c31\u662f\u901b\u4e66\u5e97\u3002\u6211\u7ecf\u5e38\u5728\u4e66\u5e97\u653e\u6570\u5b66\u4e66\u7684\u5730\u65b9\u6d41\u8fde\u3001\u968f\u5174\u6d4f\u89c8\u3002<\/p>\n

\u5218:\u8fd9\u8ba9\u6211\u60f3\u5230\u9a6c\u514b\u2022\u5410\u6e296\u7684\u8bdd:\u300e\u6211\u7edd\u4e0d\u8ba9\u5b66\u6821\u7684\u8bfe\u4e1a\u5e72\u6270\u6211\u7684\u6559\u80b2\u3002\u300f\u6240\u4ee5\u4f60\u4e0d\u592a\u53d7\u5230\u5927\u5b66\u5165\u5b66\u8003\u8bd5\u7684\u7f81\u7eca,\u8003\u8bd5\u5bf9\u4f60\u800c\u8a00\u5f88\u5bb9\u6613?<\/p>\n

\u6df1\u8c37:\u4e0d\u5bb9\u6613\u3002\u4e0d\u8fc7\u4e0d\u7ba1\u5982\u4f55 ,\u6211\u8003\u4e0a\u4e86 ,\u8fd9\u5c31\u591f\u4e86\u3002<\/p>\n

\u5218:\u4f46\u4f60\u82b1\u4e86\u4e0d\u5c11\u65f6\u95f4\u53bb\u505a\u4e0e\u51c6\u5907\u8003\u8bd5\u65e0\u5173\u7684\u4e8b\u3002<\/p>\n

\u6df1\u8c37:\u662f\u82b1\u4e86\u4e9b\u65f6\u95f4,\u662f\u4e0d\u5927\u597d ,\u6211\u7684\u82f1\u6587\u6210\u7ee9\u5c31\u5f88\u7cdf\u3002<\/p>\n

\u90d1:\u53ef\u662f\u4f60\u8fd8\u662f\u8fdb\u4e86\u4e1c\u4eac\u5927\u5b66\u3002<\/p>\n

\u5218:\u8fdb\u4e86\u4e1c\u5927\u4e4b\u540e\u90fd\u505a\u4e9b\u4ec0\u4e48\u5462?\u4f60\u5df2\u7ecf\u5ff5\u4e86 Riesz-Nagy, J. Kelley\u8fd8\u6709 van der Waer\u00adden\u3002\u5728\u4e1c\u5927\u8fd8\u5ff5\u4e9b\u4ec0\u4e48?\u6df1\u8c37:\u8d77\u5148\u5c1d\u8bd5\u4e86\u8bb8\u591a\u4e8b\u3002\u5927\u90e8\u5206\u7684\u6570\u5b66\u4e66\u662f\u5927\u4e8c\u5ff5\u7684 ,\u90a3\u65f6\u5f00\u59cb\u770b\u82f1\u6587\u4e66 ,\u53d1\u73b0\u6709\u8bb8\u591a\u53ef\u4ee5\u5ff5\u7684\u4e66 ,\u540e\u6765\u5c31\u6ca1\u6709\u90a3\u4e48\u591a\u65f6\u95f4\u9605\u8bfb\u4e86\u3002\u73b0\u5728\u4e00\u6b21\u9876\u591a\u53ea\u80fd\u770b\u4e00\u672c\u4e66\u3002<\/p>\n

\u5218:\u6211\u60f3\u95ee\u7684\u662f\u5f53\u65f6\u4f60\u6709\u6ca1\u6709\u5927\u5b66\u90e8\u7684\u6570\u5b66\u8bfe\u7a0b\u53ef\u4ee5\u4fee ?\u56e0\u4e3a\u90a3\u4e9b\u4e1c\u897f\u4f60\u65e9\u5c31\u81ea\u5b66\u8fc7\u4e86\u3002<\/p>\n

\u6df1\u8c37:\u542c\u542c\u8bfe\u603b\u662f\u597d\u7684\u3002\u5927\u4e09\u3001\u5927\u56db\u6709\u4e9b\u8bfe\u8fd8\u662f\u6ee1\u6709\u7528\u7684\u3002<\/p>\n

\u5218:\u539f\u6765\u8fd9\u6837\u3002\u4f60\u662f\u6211\u6240\u77e5\u9053\u7b2c\u4e00\u4e2a\u5728\u9ad8\u4e2d\u5c31\u8bfb\u4e86 van der Waerden\u548c J. Kelley\u7684\u4e66\u7684\u4eba\u3002<\/p>\n

\u6df1\u8c37:\u867d\u7136\u6211\u8bf4\u90a3\u4e9b\u4e66\u662f\u5728\u9ad8\u4e2d\u65f6\u8bfb\u7684,\u5b9e\u9645\u4e0a\u662f\u5728\u9ad8\u4e2d\u6bd5\u4e1a\u540e\u7b49\u7740\u4e0a\u5927\u5b66\u7684\u51e0\u4e2a\u6708\u7a7a\u6863\u4e2d\u5ff5\u7684\u3002<\/p>\n

\u6c5f\u5b5f\u84c9 (\u4ee5\u4e0b\u7b80\u79f0\u300c\u6c5f\u300d):\u6240\u4ee5\u4f60\u5728\u4e24\u4e2a\u6708\u5ff5\u5b8c\u4e86\u4e24\u672c\u4e66 ?!<\/p>\n

\u6df1\u8c37:\u6ca1\u9519\u3002<\/p>\n

\u90d1:\u4e3b\u4fee\u6570\u5b66\u7684\u5b66\u751f\u9700\u8981\u4fee\u591a\u5c11\u95e8\u8bfe\u5462?\u6df1\u8c37:\u7b2c\u4e00\u5e74\u5417?\u53ea\u6709\u5fae\u79ef\u5206\u548c\u4ee3\u6570\u3002<\/p>\n

\u90d1:\u4e0d\u662f\u5927\u4e09\u624d\u5f00\u59cb\u5206\u79d1\u7cfb\u5417?<\/p>\n

\u6df1\u8c37:\u90a3\u65f6\u5019\u5927\u4e09\u751f\u4ece\u661f\u671f\u4e00\u5230\u661f\u671f\u56db\u6bcf\u5929\u90fd\u6709\u4e09\u4e2a\u5c0f\u65f6\u7684\u6570\u5b66\u8bfe\u4ee5\u53ca 90\u5206\u949f\u7684\u6f14\u4e60\u8bfe\u3002\u4e24\u95e8\u5206\u6790\u3001\u4e00\u95e8\u4ee3\u6570\u3001\u4e00\u95e8\u51e0\u4f55\u8fd9\u6837\u4e0a\u4e86\u4e00\u5e74,\u8fd9\u662f\u4e1c\u5927\u7684\u6807\u51c6\u8bfe\u7a0b\u3002\u4eac\u90fd\u5927\u5b66\u5219\u662f\u76f8\u5bf9\u81ea\u7531\u7684\u5b66\u6821,\u4f46\u4ed6\u4eec\u8fd8\u662f\u6709\u8fd9\u4e00\u7c7b\u4e25\u683c\u800c\u7d27\u51d1\u7684\u8bfe\u7a0b\u3002<\/p>\n

\u5218:\u53f0\u6e7e\u5927\u5b66\u7684\u8bfe\u7a0b\u4e5f\u662f\u975e\u5e38\u91cd\u3002\u4f46\u6211\u53d1\u73b0\u8fd9\u6837\u7684\u8bfe\u7a0b ,\u9002\u5408\u50cf\u4f60\u8fd9\u6837\u51fa\u8272\u7684\u5b66\u751f,\u5374\u4e0d\u89c1\u5f97\u9002\u5408\u4e00\u822c\u7684\u5b66\u751f\u3002\u4f60\u4e0d\u8fd9\u6837\u89c9\u5f97\u5417?<\/p>\n

\u6df1\u8c37:\u6211\u89c9\u5f97\u7d27\u51d1\u7684\u8bfe\u7a0b\u65e0\u8bba\u5982\u4f55\u662f\u597d\u7684\u3002\u56e0\u4e3a\u5982\u679c\u6ca1\u6709\u8fd9\u6837\u7d27\u51d1\u7684\u8bfe\u7a0b ,\u9664\u975e\u4f60\u5f88\u806a\u660e,\u5426\u5219\u6ca1\u6709\u529e\u6cd5\u597d\u597d\u5229\u7528\u65f6\u95f4\u5b9e\u5728\u7684\u5b66\u70b9\u4e1c\u897f\u3002\u5927\u90e8\u5206\u4ece\u4e1c\u5927\u6bd5\u4e1a\u7684\u6570\u5b66\u5bb6 ,\u4e0d\u7ba1\u4e13\u95e8\u9886\u57df\u662f\u4ec0\u4e48,\u90fd\u61c2\u4e00\u4e9b\u62d3\u6734,\u4e00\u4e9b\u6cdb\u51fd,\u4e00\u4e9b Galois\u7406\u8bba\u3002\u8981\u540c\u65f6\u77e5\u9053\u8fd9\u4e09\u4e2a\u9886\u57df,\u901a\u5e38\u4e0d\u662f\u90a3<\/p>\n

6\u8bd1\u6ce8 :\u539f\u6587 Mark Twain has said \u2019I never let my schooling to interfere with my education.\u2019
\n<\/p>\n

\u4e48\u5bb9\u6613\u3002\u8fd9\u6837\u7684\u8bfe\u7a0b\u8ba9\u4eba\u53ef\u4ee5\u540c\u65f6\u5b66\u5230\u4e09\u6837\u4e1c\u897f,\u867d\u7136\u4e0d\u77e5\u9053\u5b66\u751f\u53ef\u4ee5\u4e86\u89e3\u591a\u5c11 ,\u4f46\u8d77\u7801\u53ef\u4ee5\u5b66\u5230\u4e00\u4e9b\u57fa\u7840\u3002<\/p>\n

\u5218:\u6700\u8d77\u7801\u63d0\u4f9b\u4e86\u4e00\u4e2a\u673a\u4f1a\u3002<\/p>\n

\u6df1\u8c37:\u81f3\u5c11\u90a3\u4e9b\u540e\u6765\u6210\u4e3a\u6570\u5b66\u5bb6\u7684\u4e1c\u5927\u6bd5\u4e1a\u751f\u662f\u4e86\u89e3\u7684\u3002\u5927\u90e8\u5206\u7684\u6570\u5b66\u5bb6\u5728\u6210\u4e3a\u6570\u5b66\u5bb6\u4e4b\u540e\u627e\u4e0d\u51fa\u65f6\u95f4\u53e6\u5916\u53bb\u5b66\u90a3\u4e9b\u79d1\u76ee\u3002\u53e6\u4e00\u65b9\u9762,\u90a3\u65f6\u5019\u5b66\u7684\u5927\u90e8\u5206\u5185\u5bb9\u5728\u5f53\u4e0b\u7528\u4e0d\u4e0a ,\u90fd\u662f\u4e4b\u540e\u624d\u80fd\u7528\u4e0a\u7684\u3002\u6211\u5f88\u5e78\u8fd0\u540e\u6765\u90fd\u7528\u4e0a\u4e86\u3002\u62d3\u6734\u662f\u5df2\u7ecf\u7528\u5230\u7684,\u521a\u5f00\u59cb\u505a\u7814\u7a76\u7684\u65f6\u5019\u79bb\u4ee3\u6570\u5f88\u8fdc, \u6e10\u6e10\u5730\u8d8a\u6765\u8d8a\u8fd1, \u6211\u5f88\u9ad8\u5174\u53ef\u4ee5\u7528\u5230\u4ee3\u6570\u3002<\/p>\n

\u5218:\u5728\u8bbf\u8c08\u4e4b\u524d\u6211\u4eec\u804a\u5230\u4e86 Charles Conley7 ,\u6211\u4ece 1972\u5e74\u5c31\u8ba4\u8bc6\u4ed6\u4e86 ,\u6709\u4e00\u6b21\u4ed6\u8bf4\u4ed6\u5728\u5b66\u4ee3\u6570,\u6211\u95ee\u4ed6 :\u300e\u4f60\u9700\u8981\u7528\u5230\u4ee3\u6570\u5417?\u300f\u4ed6\u56de\u7b54:\u300e\u5982\u679c\u6211\u4e0d\u4f1a,\u5c31\u6c38\u8fdc\u4e0d\u4f1a\u6709\u8fd9\u4e2a\u9700\u8981\u3002\u300f\u6240\u4ee5\u6211\u80fd\u95ee\u4e00\u4e2a\u6bd4\u8f83\u4e13\u4e1a\u7684\u95ee\u9898\u5417?\u4f60\u94bb\u7814 Arnold\u2019s Conjecture,\u800c\u4e14\u6709\u5341\u5206\u91cd\u8981\u7684\u5de5\u4f5c,\u6211\u542c\u8bf4 Conley\u4e5f\u5728\u505a\u8fd9\u65b9\u9762\u7684\u7814\u7a76,\u4ed6\u5728\u8fd9\u4e2a\u9886\u57df\u662f\u5728\u4ec0\u4e48\u6837\u7684\u4f4d\u7f6e?<\/p>\n

\u6df1\u8c37:\u6211\u8ba4\u4e3a Conley\u8bc1\u660e\u4e86\u975e\u5e38\u91cd\u8981\u7684\u4e00\u90e8\u5206\u3002\u4ed6\u548c Zehnder8\u8bc1\u660e\u4e86\u8f6e\u80ce\u9762\u7684\u60c5\u51b5\u3002\u6211\u60f3\u90a3\u662f\u7b2c\u4e00\u6b65,\u7b2c\u4e00\u6b65\u603b\u662f\u5f88\u91cd\u8981\u7684\u3002\u4ed6\u4eec\u7684\u5de5\u4f5c\u544a\u8bc9\u4e86\u5927\u5bb6\u8fd9\u4e2a\u95ee\u9898\u662f\u53ef\u4ee5\u505a\u7684\u3002\u4e5f\u8bb8\u4ece\u90a3\u4e4b\u540e,\u4eba\u4eec\u6108\u6765\u6108\u91cd\u89c6\u8fd9\u4e2a\u95ee\u9898\u3001\u5c1d\u8bd5\u8981\u89e3\u51b3\u5b83\u3002\u90a3\u4e4b\u524d ,\u6211\u4e0d\u786e\u5b9a\u6709\u591a\u5c11\u4eba\u8ba4\u771f\u770b\u5f85 Arnold\u2019s Conjecture\u3002\u5728\u6570\u5b66\u4e0a ,\u4f60\u63d0\u51fa\u4e00\u4e9b\u56f0\u96be\u7684\u95ee\u9898,\u5f00\u59cb\u65f6,\u95ee\u9898\u770b\u8d77\u6765\u4f3c\u4e4e\u9065\u4e0d\u53ef\u53ca ,\u751a\u81f3\u6ca1\u6709\u4eba\u5c1d\u8bd5\u7740\u53bb\u89e3\u51b3\u5b83\u3002\u7136\u540e\u65f6\u673a\u6210\u719f\u4e86,\u4eba\u4eec\u5f00\u59cb\u5173\u6ce8\u8fd9\u4e2a\u95ee\u9898\u3002Conley & Zehnder\u2019s\u7684\u5de5\u4f5c, Floer9\u7684\u5de5\u4f5c,\u5728\u5341\u5e74\u5185\u9646\u7eed\u51fa\u73b0,\u5c06\u8fd9\u4e2a\u95ee\u9898\u4ece\u6211\u4eec\u65e0\u6cd5\u64bc\u52a8\u53d8\u6210\u6211\u4eec\u6709\u80fd\u529b\u53ef\u4ee5\u53bb\u505a\u7684,\u8fd9\u6bb5\u65f6\u95f4\u662f\u5173\u952e\u7684\u65f6\u523b\u3002<\/p>\n

\u5218:\u6240\u4ee5\u4f60\u4e0d\u662f\u5f88\u786e\u5b9a Arnold\u81ea\u5df1\u521d\u671f\u5bf9\u8fd9 Conjecture\u6709\u591a\u5927\u7684\u4f53\u4f1a?<\/p>\n

\u6df1\u8c37:\u6211\u4e0d\u77e5\u9053\u3002\u5728 Arnold\u6d3b\u8dc3\u7684\u65f6\u5019,\u6211\u6ca1\u6709\u89c1\u8fc7\u4ed6,\u4e0d\u77e5\u9053\u4ed6\u662f\u600e\u4e48\u6837\u7684\u4eba\u3002\u4e5f\u8bb8\u4ed6\u662f\u4e2a\u63a2\u9669\u5bb6\u5e76\u4e14\u5f88\u6709\u81ea\u4fe1\u3002\u4f46\u662f,\u5f53\u65f6\u5728\u8f9b\u51e0\u4f55\u4e2d\u6ca1\u6709\u4efb\u4f55\u9002\u5f53\u7684\u65b9\u6cd5\u3001\u60f3\u6cd5\u53ef\u4ee5\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u3002<\/p>\n

\u5218:\u6211\u89c1\u8fc7 Arnold\u51e0\u6b21 ,\u4ed6\u662f\u4f4d\u6ee1\u6709\u4e2a\u6027\u7684\u4eba\u3002<\/p>\n

\u6df1\u8c37:\u554a!\u8bf7\u522b\u544a\u8bc9\u4ed6\u6211\u521a\u521a\u8bf4\u8fc7\u7684\u8bdd\u3002<\/p>\n

\u5218:\u54e6! Arnold\u4e0e\u4f17\u4e0d\u540c\u7684\u5730\u65b9\u5c31\u5728\u4e8e\u4ed6\u53ea\u8bf4\u4e0d\u542c,\u4f46\u4ed6\u5e94\u8be5\u4f1a\u6b23\u8d4f\u4f60\u7684\u610f\u89c1\u3002\u4ed6\u662f\u4e2a\u5f88\u6709\u610f\u601d\u7684\u4eba\u3002<\/p>\n

\u6df1\u8c37:\u4e0d\u8fc7\u4ed6\u5f53\u7136\u662f\u4f4d\u5f88\u91cd\u8981\u7684\u6570\u5b66\u5bb6\u3002 Arnold\u63d0\u8fc7\u51e0\u4e2a\u95ee\u9898,\u4ed6\u662f\u7b2c\u4e00\u4f4d\u63d0\u51fa\u5927\u57df\u8f9b\u51e0\u4f55 (globalsymplectic geometry)\u4e2d\u6709\u4e9b\u5f88\u6709\u8da3\u7684\u4e1c\u897f,\u5426\u5219 ,\u6ca1\u6709\u4eba\u77e5\u9053\u8be5\u600e\u4e48\u53bb\u7528\u5b83\u3002<\/p>\n

\u90d1:\u4f60\u662f\u4ec0\u4e48\u65f6\u5019\u4ea7\u751f\u6709\u5173 A\u221e<\/sup>\u4ee3\u6570\u7ed3\u6784\u7684\u60f3\u6cd5 ?
\n7.\u8bd1\u6ce8 : Charles C. Conley(1933-1984),\u7f8e\u56fd\u6570\u5b66\u5bb6\u3002 8\u8bd1\u6ce8 : Eduard Zehnder(1940-),\u745e\u58eb\u6570\u5b66\u5bb6\u3002 9\u8bd1\u6ce8 : Andreas Floer(1956-1991),\u5fb7\u56fd\u6570\u5b66\u5bb6 ,\u63d0\u51fa\u540e\u6765\u53eb Floer\u540c\u8c03\u7684\u89c2\u5ff5\u3002
\n<\/p>\n

\u6df1\u8c37: 90\u5e74\u4ee3\u521d ,\u6211\u5bf9Floer\u540c\u8c03(Floerhomology)\u7684\u4e00\u4e9b\u4e1c\u897f\u6709\u5174\u8da3,\u5927\u7ea692\u621693\u5e74\u5f97\u5230 A\u221e<\/sup>\u4ee3\u6570\u8303\u7574 (A\u221e\u00a0<\/sup>algebra category)\u7684\u7ed3\u679c\u3002\u90a3\u65f6 Donaldson10<\/sup>\u505a\u4e86\u4e00\u4e9b Floer\u540c\u8c03\u7684 gauge theory\u7684\u5de5\u4f5c,\u5728\u4e00\u4e2a\u6f14\u8bb2\u4e2d\u4ed6\u63d0\u8bae\u5efa\u6784\u67d0\u7c7b category;\u6307\u51fa\u95ee\u9898\u5728\u4e8e\u6211\u4eec\u78b0\u5230\u7684\u6709\u65f6\u662f chain complex,\u6709\u65f6\u662f Lagrangian\u6d41\u5f62 ,\u5fc5\u9700\u627e\u4e2a\u8fd9\u4e8c\u79cd\u4e1c\u897f\u7684\u6df7\u5408\u7269,\u800c\u8fd9 category\u4e0a\u7684functor\u6b63\u662f\u7b54\u6848\u3002\u62b1\u6b49,\u4f3c\u4e4e\u592a\u6280\u672f\u6027\u4e86\u3002\u603b\u4e4b,\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u8981\u7528 category\u3002\u5bf9\u975e\u7ebf\u6027\u73b0\u8c61,\u4eba\u4eec\u5f15\u7528\u975e\u7ebf\u6027\u5206\u6790\u5230\u51e0\u4f55\u4ee5\u53ca\u62d3\u6734,Donaldson\u7b49\u4eba\u627e\u5230\u67d0\u79cd\u201c\u6570\u201d\u6765\u533a\u5206\u4e8b\u7269, Floer\u66f4\u8fdb\u4e00\u6b65\u6784\u7b51\u4e86\u201c\u7fa4\u201d,\u8ba9\u6211\u611f\u89c9\u4ee3\u6570\u5728\u8fd9\u4e2a\u95ee\u9898\u4e2d\u6709\u66f4\u5927\u7684\u89d2\u8272\u3002\u51e0\u4f55\u5f88\u6709\u8da3\u800c\u4e14\u6709\u8bb8\u591a\u76f4\u89c2,\u4f46\u96be\u4ee5\u9a7e\u9a6d,\u4ee3\u6570\u5219\u53ef\u4ee5\u7b97\u800c\u6613\u4e8e\u4e0b\u624b,\u56e0\u6b64\u60f3\u4e86\u89e3\u51e0\u4f55,\u628a\u51e0\u4f55\u73b0\u8c61\u8f6c\u6362\u6210\u4ee3\u6570\u7684\u4e1c\u897f\u6765\u505a\u5c31\u5f88\u81ea\u7136,\u800c\u62d3\u6734\u4e5f\u8ddf\u7740\u6765\u4e86\u3002 Floer\u66fe\u8bf4\u4ee3\u6570\u62d3\u6734\u5c31\u662f\u4ee5\u4ee3\u6570\u6765\u8868\u793a\u62d3\u6734\u7684\u6027\u8d28\u3002\u5728\u6211\u4eec\u5f00\u59cb\u63a2\u8ba8\u975e\u7ebf\u6027 Floer\u7406\u8bba\u65f6\u53d1\u73b0\u6211\u4eec92\u5e74\u5f97\u5230\u7684 category\u6070\u6070\u6b63\u662f\u8fd9\u91cc\u6240\u9700\u8981\u7684\u3002<\/p>\n

\u5218:\u8ba9\u6211\u4eec\u56de\u5230\u6559\u80b2\u65b9\u9762\u3002\u4ece\u4f60\u521a\u521a\u63d0\u5230\u7684,\u4f60\u7684\u5b66\u4e60\u529b\u5f88\u5f3a ,\u53ef\u4ee5\u85c9\u7531\u4e66\u672c\u81ea\u4fee\u53c8\u8ba4\u540c\u4e1c\u5927\u8fd9\u6837\u9ad8\u6c34\u5e73\u3001\u624e\u5b9e\u7684\u57fa\u7840\u8bfe\u7a0b ,\u4f60\u5982\u4f55\u770b\u5f85\u76ee\u524d\u4eac\u90fd\u5927\u5b66\u7684\u5b66\u751f?<\/p>\n

\u6df1\u8c37:\u4eac\u90fd\u5927\u5b66\u554a!\u6211\u521a\u5230\u4eac\u90fd\u5927\u5b66\u7684\u65f6\u5019,\u8bfe\u7a0b\u975e\u5e38\u6709\u5f39\u6027\u3002\u5b66\u751f\u53ef\u4ee5\u81ea\u7531\u9009\u8bfe ,\u4e5f\u53ef\u4ee5\u81ea\u7531\u7684\u4e0d\u9009\u8bfe\u3002\u4f46\u662f\u5df2\u7ecf\u8fc7\u4e16\u7684 Maruyama\u6559\u6388\u5efa\u7acb\u4e86\u4e00\u4e2a\u5236\u5ea6 \u2014\u6bcf\u4e2a\u5b66\u751f\u90fd\u5fc5\u987b\u8981\u4e0a\u4e00\u4e9b seminar\u3002\u6211\u544a\u8bc9\u4ed6:\u300e\u8fd9\u662f\u4e1c\u5927\u8bad\u7ec3\u5b66\u751f\u7684\u65b9\u5f0f ,\u4eac\u90fd\u5927\u5b66\u5219\u662f\u53e6\u4e00\u4e2a\u6781\u7aef,\u5b8c\u5168\u4e0d\u7ea6\u675f\u5b66\u751f,\u4e3a\u4ec0\u4e48\u4f60\u60f3\u6539\u53d8\u5462?\u300f Maruyama\u6559\u6388\u5219\u8bf4:\u300e\u8fc7\u53bb,\u8ba9\u5b66\u751f\u6bcf\u5929\u90fd\u5f88\u81ea\u7531,\u6709\u4e00\u4e9b,\u4e5f\u8bb8\u4e00\u3001\u4e8c\u4f4d\u5b66\u751f\u4f1a\u5229\u7528\u8fd9\u4e9b\u7a7a\u95f2,\u505a\u4e9b\u6709\u610f\u4e49\u7684\u4e8b\u3002\u800c\u73b0\u5728,\u5982\u679c\u4f60\u653e\u4efb\u5b66\u751f\u81ea\u7531,\u5c31\u4e0d\u4f1a\u6709\u4eba\u6765\u4e0a\u8bfe,\u6240\u4ee5\u4f60\u4e00\u5b9a\u8981\u7ed9\u4ed6\u4eec\u4e00\u4e9b\u529f\u8bfe\u3002\u300f\u5373\u4fbf\u5982\u6b64,\u8fd8\u662f\u6709\u4e9b\u5dee\u5f02,\u4e3e\u4f8b\u6765\u8bf4,\u5982\u679c\u4e00\u4e2a\u5b66\u751f\u60f3\u4fee\u4e00\u95e8\u8bfe ,\u4ed6\u53ef\u4ee5\u9009\u62e9\u5728\u5927\u4e8c\u3001\u5927\u4e09\u6216\u5927\u56db\u7684\u65f6\u5019\u4fee\u3002\u6211\u6709\u4e00\u6b21\u5c31\u5f88\u60ca\u8bb6,\u6709\u4e00\u4f4d\u56db\u5e74\u7ea7\u7684\u5b66\u751f\u5728\u6211\u6559\u6d41\u578b\u5bfc\u8bba\u7684\u65f6\u5019\u6765\u8003\u8bd5\u3002\u7531\u6b64\u53ef\u89c1\u4eac\u90fd\u5927\u5b66\u5728\u8fd9\u65b9\u9762\u5b9e\u5728\u5f88\u6709\u5f39\u6027\u3002\u4e1c\u4eac\u5927\u5b66\u6570\u5b66\u7cfb\u61c2\u5f97\u8db3\u591f kinetic dynamics\u7684\u5b66\u751f\u6bd4\u4eac\u90fd\u5927\u5b66\u5c11\u5f88\u591a,\u56e0\u4e3a\u7269\u7406\u4e0e\u6570\u5b66\u5728\u4e1c\u4eac\u5927\u5b66\u662f\u5206\u5f00\u7684\u3002\u6211\u5b66\u4e86\u8f9b\u51e0\u4f55\u4f46\u662f\u6211\u4ece\u6765\u6ca1\u4fee\u8fc7 kinetic dynamics\u7684\u8bfe\u3002\u4eac\u90fd\u4eba\u603b\u8bf4\u4eac\u90fd\u5927\u5b66\u662f\u81ea\u7531\u5f00\u653e\u7684\u5927\u5b66\u3002<\/p>\n

\u5218:\u6240\u4ee5\u5927\u5b66\u5165\u5b66\u8003\u6ca1\u6709\u7ed9\u4f60\u592a\u591a\u75db\u82e6\u3002\u6211\u542c\u5230\u5f88\u591a\u4eba\u62b1\u6028\u5165\u5b66\u8003\u8bd5\u7684\u79cd\u79cd ,\u4f46\u662f\u5bf9\u4e8e\u4f60,\u8fd9\u4e0d\u6210\u95ee\u9898,\u4f60\u53ea\u82b1\u4e86\u5f88\u5c11\u7684\u529b\u6c14\u3002<\/p>\n

\u6df1\u8c37:\u4f46\u6211\u4e00\u70b9\u90fd\u4e0d\u559c\u6b22\u3002<\/p>\n

\u5218:\u4e0d\u8fc7\u4f60\u5e76\u6ca1\u6709\u56e0\u6b64\u53d7\u5230\u714e\u71ac ?<\/p>\n

\u6df1\u8c37:\u6211\u4e0d\u77e5\u9053\u75db\u82e6\u7684\u7a0b\u5ea6\u3002\u4f46\u8003\u8fc7\u4e86,\u6240\u4ee5\u8fd8\u7b97\u53ef\u4ee5\u63a5\u53d7\u3002\u4e0d\u8fc7\u6211\u89c9\u5f97\u6570\u5b66\u8fd9\u95e8\u5b66\u79d1\u8fd8\u662f\u53d7\u5230\u4f24\u5bb3,\u8bb8\u591a\u65e5\u672c\u4eba\u4e0d\u559c\u6b22\u6570\u5b66,\u56e0\u4e3a\u5927\u5b66\u8003\u8bd5\u7684\u6570\u5b66\u7ed9\u4e86\u4ed6\u4eec\u75db\u82e6\u7684\u7ecf\u9a8c\u3002\u6240\u4ee5\u6570\u5b66\u5bf9\u8bb8\u591a\u65e5\u672c\u4eba\u800c\u8a00\u662f\u4e2a\u68a6\u9b47\u3002<\/p>\n

10. \u8bd1\u6ce8 : Simon K. Donaldson(1957-),\u82f1\u56fd\u6570\u5b66\u5bb6 ,\u4ee5\u4ed6\u5728\u5e73\u6ed1\u56db\u7ef4\u6d41\u5f62\u62d3\u6734\u7684\u5de5\u4f5c\u800c\u8457\u540d\u3002
\n<\/p>\n

\u5218:\u6211\u60f3\u9664\u4e86\u4f60\u4e4b\u5916 ,\u6570\u5b66\u662f\u56f0\u96be\u7684,\u8fd9\u662f\u653e\u8bf8\u56db\u6d77\u7686\u51c6\u7684\u3002<\/p>\n

\u6df1\u8c37:\u5982\u4f60\u6240\u8bf4\u6570\u5b66\u662f\u56f0\u96be\u7684\u3002\u4f46\u5982\u679c\u5148\u6709\u7279\u5b9a\u7684\u76ee\u6807\u6216\u5174\u8da3\u800c\u53bb\u5b66\u4e60,\u5c31\u53ef\u4ee5\u662f\u559c\u60a6\u800c\u6709\u8da3\u7684\u3002\u95ee\u9898\u662f,\u6570\u5b66\u662f\u5927\u5b66\u5165\u5b66\u8003\u8bd5\u5fc5\u987b\u8981\u901a\u8fc7\u7684\u79d1\u76ee,\u901a\u5e38\u8fd9\u5c31\u662f\u75db\u82e6\u7684\u6765\u6e90\u3002\u6211\u60f3\u8fd9\u662f\u4eba\u4eec\u4e0d\u559c\u6b22\u6570\u5b66\u7684\u539f\u56e0\u3002<\/p>\n

\u5218:\u6211\u66fe\u7ecf\u5bf9\u65e5\u672c\u6570\u5b66\u6709\u4e9b\u65e2\u5b9a\u5370\u8c61,\u4e0d\u77e5\u9053\u4f60\u89c9\u5f97\u65e5\u672c\u7684\u6570\u5b66\u6709\u54ea\u4e9b\u7279\u8d28?\u6709\u54ea\u4e9b\u7279\u8d28\u4f1a\u8ba9\u4f60\u89c9\u5f97\u300e\u54e6!\u8fd9\u5c31\u662f\u65e5\u672c\u6570\u5b66\u5bb6\u7684\u7814\u7a76\u3002\u300f\u6709\u8fd9\u6837\u7684\u7279\u8d28\u5417 ?<\/p>\n

\u6df1\u8c37:\u6211\u4eec\u66fe\u7ecf\u8c08\u8fc7\u8fd9\u7c7b\u7684\u4e8b\u60c5\u3002\u65e5\u672c\u6570\u5b66\u5bb6\u5728\u6210\u5343\u4e0a\u4e07\u7684\u95ee\u9898\u4e2d\u770b\u5230\u4e00\u4e2a\u9898\u76ee,\u5c31\u4e13\u6ce8\u7684\u505a\u8fd9\u4e2a\u9898\u76ee\u5e76\u4ece\u4e2d\u5f97\u5230\u6ee1\u8db3,\u4f46\u6709\u4e9b\u4eba\u559c\u6b22\u505a\u4e00\u822c\u6027,\u5e7f\u4e49\u7684\u9898\u76ee\u3002\u5c31\u62ff Kiyoshi Oka11<\/sup>\u548c Henri Cartan12<\/sup>\u6765\u8bf4, Oka\u53d1\u73b0 coherent sheaf\u4e00\u4e9b\u6700\u57fa\u672c\u3001\u6700\u7d27\u8981\u7684\u6027\u8d28\u3002(Oka\u5e76\u4e0d\u559c\u6b22 coherent sheaf\u8fd9\u4e2a\u540d\u8bcd\u3002)\u5f53\u7136 Cartan\u662f\u5927\u6570\u5b66\u5bb6 ,\u4ed6\u53d1\u5c55\u4e86\u6574\u5957 coherent sheaf\u7684\u7406\u8bba,\u5e76\u4e14\u53ef\u4ee5\u5e94\u7528\u5230\u8bb8\u591a\u5176\u5b83\u7684\u9886\u57df,\u50cf\u4ee3\u6570\u51e0\u4f55\u3001\u4ee3\u6570\u62d3\u6734\u3002 Oka\u5728\u67d0\u79cd\u7a0b\u5ea6\u4e0a\u53ea\u5904\u7406\u95ee\u9898\u4e2d\u6700\u57fa\u672c,\u6700\u8981\u7d27\u7684\u90e8\u4efd\u3002\u4e24\u8005\u6709\u6781\u5927\u7684\u5bf9\u6bd4,\u4f46\u662f\u90fd\u5f88\u91cd\u8981\u3002<\/p>\n

\u5218:\u6240\u4ee5\u65e5\u672c\u4eba\u503e\u5411\u4ee5\u660e\u786e\u7684\u65b9\u5f0f\u4f5c\u6570\u5b66,\u6211\u8fd9\u6837\u8bf4\u5bf9\u5417?<\/p>\n

\u6df1\u8c37:\u4e0d\u662f\u660e\u786e\u5730,\u800c\u662f\u9762\u5bf9\u95ee\u9898\u65f6,\u5c31\u53ea\u4e13\u6ce8\u4e8e\u95ee\u9898\u4e2d\u4ed6\u8ba4\u4e3a\u6700\u7d27\u8981\u7684\u90e8\u5206\u3002<\/p>\n

\u5218:\u5173\u952e\u7684\u95ee\u9898\u3002<\/p>\n

\u6df1\u8c37:\u662f\u7684 ,\u5173\u952e\u5904\u3002\u5f53\u7136\u4e5f\u6709\u5176\u4ed6\u7c7b\u578b\u7684\u65e5\u672c\u6570\u5b66\u5bb6 ,\u4f46\u5f88\u5c11\u3002<\/p>\n

\u5218:\u5f53\u7136 ,\u6cd5\u56fd\u7684\u6570\u5b66\u4e5f\u5e38\u88ab\u6279\u8bc4\u4e3a\u592a\u4e00\u822c\u6027\u3002\u6279\u8bc4 Bourbaki13<\/sup>\u7684\u4e66\u592a\u62bd\u8c61,\u4f46\u662f Oka\u7684\u5de5\u4f5c\u5960\u5b9a\u591a\u53d8\u91cf\u590d\u5206\u6790\u7684\u57fa\u7840\u5e76\u4e14\u5e7f\u4e3a\u540e\u6765\u7684\u6570\u5b66\u5bb6\u6240\u8d5e\u53f9,\u8fd9\u662f\u5f88\u6e05\u695a\u7684,\u4e0d\u662f\u5417?<\/p>\n

\u6df1\u8c37:\u6211\u76f8\u4fe1\u5982\u6b64\u3002Oka\u5728\u65e5\u672c\u5f53\u7136\u5f88\u6709\u540d,\u4e0d\u8fc7\u5728\u5176\u5b83\u56fd\u5bb6 ,\u6211\u5c31\u4e0d\u786e\u5b9a\u4e86\u3002\u4f60\u95ee\u7f8e\u56fd\u6570\u5b66\u5bb6 ,\u4e5f\u8bb8\u4ed6\u4eec\u4f1a\u77e5\u9053\u3002<\/p>\n

\u5218:\u4f60\u5e94\u8be5\u95ee\u9876\u5c16\u7684\u6570\u5b66\u5bb6 ,\u662f\u4e0d?\u800c\u4e0d\u662f\u4e00\u822c\u7684\u6570\u5b66\u5bb6 ,\u4e00\u822c\u6570\u5b66\u5bb6\u53ea\u4f1a\u5faa\u7740\u524d\u4eba\u7684\u7ecf\u9a8c\u5f80\u4e0b\u505a ,\u800c\u4e0d\u53bb\u63a2\u7a76\u6e90\u5934,\u4ed6\u4eec\u6ca1\u6709\u8fd9\u79cd\u80fd\u529b\u3002\u4f60\u6709\u6ca1\u6709\u8fc7\u300e\u6211\u5e0c\u671b\u81ea\u5df1\u4e0d\u662f\u505a\u8fd9\u95e8\u7814\u7a76,\u5b81\u613f\u505a\u4e9b\u522b\u7684\u300f\u7684\u5ff5\u5934?\u6211\u89c9\u5f97\u4f60\u4f3c\u4e4e\u5f88\u7b03\u5b9a\u77e5\u9053\u81ea\u5df1\u8981\u505a\u4ec0\u4e48\u3002<\/p>\n

\u6df1\u8c37:\u6211\u53ef\u4e0d\u90a3\u4e48\u786e\u5b9a\u3002\u6211\u4e00\u76f4\u90fd\u5728\u601d\u8003\u3001\u5c1d\u8bd5\u505a\u522b\u7684\u9886\u57df\u3002<\/p>\n

\u5218:\u50cf\u751a\u4e48?<\/p>\n

\u6df1\u8c37:\u6211\u6307\u7684\u662f\u5229\u7528\u540c\u8c03\u4ee3\u6570 (homologyalgebra)\u53bb\u505a\u91cf\u5b50\u573a\u8bba (quantum \ufb01eld theory)\u3002\u6211\u73b0\u5728\u7684\u5de5\u4f5c\u4e5f\u4e0e\u8fd9\u4e2a\u6709\u5173,\u4f46\u662f\u5e0c\u671b\u80fd\u548c\u7269\u7406\u7684\u5173\u7cfb\u66f4\u76f4\u63a5\u3002\u5229\u7528\u540c\u8c03\u4ee3\u6570\u5efa\u7acb\u91cf\u5b50\u573a\u8bba\u4e25\u8c28\u7684\u6570\u5b66\u57fa\u7840\u5219\u662f\u53e6\u4e00\u79cd\u68a6\u60f3\u3002\u4e8b\u5b9e\u4e0a\u6211\u4e0d\u77e5\u9053\u751a\u4e48\u65f6\u5019\u53ef\u4ee5\u5f00\u59cb\u505a\u8fd9\u4e2a\u5de5\u4f5c\u3002\u6211\u7684\u5e74\u7eaa\u505a\u8fd9\u4e2a\u6050\u6015\u5df2\u7ecf\u8001\u4e86\u3002<\/p>\n

11<\/sup>\u8bd1\u6ce8 :\u5188\u6d01 (Kiyoshi Oka, 1901-1978),\u65e5\u672c\u6570\u5b66\u5bb6 ,\u4e0e Henri Cartan\u90fd\u662f\u591a\u53d8\u91cf\u590d\u5206\u6790\u9886\u57df\u7684\u5960\u57fa\u8005\u3002\u8be6\u89c1\u6570\u5b66\u4f20\u64ad\u7b2c 20\u5377,\u7b2c4\u671f\u3002
\n12\u8bd1\u6ce8 : Henri Cartan(1904-2008),\u6cd5\u56fd\u6570\u5b66\u5bb6 ,\u66fe\u83b7 Wolf Prize,\u6570\u5b66\u5bb6 Elie Joseph Cartan\u4e4b\u5b50\u3002\u53e6\u89c1\u8bd1\u6ce8 11\u3002 \u00b4
\n13\u8bd1\u6ce8 : Nicolas Bourbaki, 20\u4e16\u7eaa\u4e00\u7fa4\u6cd5\u56fd\u6570\u5b66\u5bb6\u7684\u7b14\u540d\u3002\u81ea1935\u5e74\u5f00\u59cb\u64b0\u5199\u4e00\u7cfb\u5217\u8ff0\u8bf4\u5bf9\u73b0\u4ee3\u9ad8\u7b49\u6570\u5b66\u63a2\u7814\u6240\u5f97\u7684\u4e66\u7c4d,\u81f4\u529b\u4e8e\u505a\u5230\u6700\u6781\u7aef\u7684\u4e25\u8c28\u548c\u6cdb\u5316,\u5efa\u7acb\u4e86\u4e9b\u65b0\u672f\u8bed\u548c\u6982\u5ff5\u3002<\/p>\n

<\/p>\n

\u5218:\u4f60\u60f3\u505a\u7684\u662f\u91cf\u5b50\u573a\u8bba\u7684\u54ea\u4e00\u65b9\u9762\u5462?<\/p>\n

\u6df1\u8c37:\u5f88\u5947\u602a\u7684,\u7269\u7406\u5b66\u5927\u90e8\u5206\u7684\u57fa\u7840\u5de5\u4f5c\u7ecf\u8fc7\u4e00\u9635\u5b50\u540e\u4f1a\u6709\u6570\u5b66\u5bb6\u4e3a\u5176\u5efa\u7acb\u4e25\u683c\u7684\u6570\u5b66\u57fa\u7840,\u50cf\u5e7f\u4e49\u76f8\u5bf9\u8bba\u6709Minkowski14\u3001\u91cf\u5b50\u529b\u5b66\u6709 von Neumann15\u7b49\u4eba\u3002\u4f46\u91cf\u5b50\u573a\u8bba\u51fa\u73b0\u5c06\u8fd150\u5e74,\u5df2\u7ecf\u6210\u4e3a\u7269\u7406\u5b66\u7684\u57fa\u7840,\u800c\u6570\u5b66\u5bb6\u8fd8\u6478\u4e0d\u7740\u8fb9,\u771f\u8ba9\u4eba\u611f\u5230\u632b\u6298\u3002<\/p>\n

\u5218:\u76ee\u524d\u6709 Glimm16\u548c Ja\ufb00e17\u7684\u7406\u8bba,\u4f46\u4ed6\u4eec\u8fd8\u65e0\u6cd5\u5b8c\u6210\u3002\u6211\u4eec\u4e5f\u66fe\u5728\u8fd9\u4e2a\u8bbf\u8c08\u7cfb\u5217\u4e2d\u8bbf\u95ee\u8fc7 Glimm\u6559\u638818\u3002\u987a\u4fbf\u63d0\u4e00\u4e0b,\u8fd9\u4e2a\u8bbf\u8c08\u4e13\u680f\u53eb\u505a\u300c\u6709\u670b\u81ea\u8fdc\u65b9\u6765\u300d ,\u5f15\u81ea\u5b54\u5b50\u3002 Glimm\u4e5f\u66fe\u5c1d\u8bd5\u91cf\u5b50\u573a\u8bba,\u4ed6\u4e00\u5f00\u59cb\u505a C*-algebra\u7684\u5de5\u4f5c,\u540e\u6765\u6709\u4eba\u544a\u8bc9\u4ed6\u8fd9\u4e0e\u91cf\u5b50\u573a\u8bba\u6709\u5173,\u4e8e\u662f\u4ed6\u8ba4\u771f\u7684\u60f3\u8981\u53bb\u505a\u91cf\u5b50\u573a\u8bba,\u4f46\u5f53\u4ed6\u8fdb\u53bb\u540e\u53d1\u73b0\u6240\u7528\u7684\u5de5\u5177\u6bd4\u8f83\u591a\u7684\u5374\u662f functional analytic path integral\u3002\u4e0d\u8bba\u5982\u4f55 ,\u8fd9\u4e2a\u5de5\u4f5c\u5c1a\u672a\u5b8c\u6210,\u6240\u4ee5\u6bcf\u4e2a\u4eba\u90fd\u8be5\u8bd5\u8bd5\u3002<\/p>\n

\u6df1\u8c37:\u6211\u60f3\u7684\u662f\u7ecf\u8fc7 80\u300190\u5e74\u4ee3,\u8bb8\u591a\u51e0\u4f55\u5185\u6db5\u90fd\u4e0e\u91cf\u5b50\u573a\u8bba\u6709\u5173,\u5c31\u50cf Glimm\u5c1d\u8bd5\u7684\u5de5\u4f5c,\u6709\u4e00\u6bb5\u65f6\u95f4\u4eba\u4eec\u4ee5\u7eaf\u7cb9\u89e3\u6790\u7684\u89c2\u70b9 ,\u4f8b\u5982\u6cdb\u51fd\u5206\u6790,C*-algebra\u6765\u601d\u8003\u91cf\u5b50\u573a\u8bba\u3002\u6211\u4eec\u591a\u5c11\u77e5\u9053\u6709\u4e9b\u573a\u8bba\u4e0e\u51e0\u4f55\u6709\u5173,\u6bd4\u65b9\u8bf4\u5f88\u53ef\u80fd\u4e0e\u5927\u57df\u51e0\u4f55 (global geometry)\u6709\u5173\u3002\u8fd9\u7c7b\u7684\u4e8b,\u8fd8\u6ca1\u6709\u5c1d\u8bd5\u8fc7 ,\u4e5f\u8bb8\u6709\u4f1f\u5927\u7684\u51e0\u4f55\u5b66\u5bb6\u8bd5\u8fc7 ,\u4e5f\u8bb8 Alain Connes19\u5df2\u7ecf\u8bd5\u8fc7\u3002\u6211\u4e0d\u77e5\u9053\u4e3a\u4ec0\u4e48\u5f53\u6211\u4eec\u505a\u8fd9\u7c7b\u51e0\u4f55\u65f6\u53ea\u7528 path integrals\u7684 trace\u3002<\/p>\n

\u90d1:\u6240\u4ee5\u4f60\u5bf9\u4e8e\u7528\u540c\u8c03\u7406\u8bba\u5904\u7406 path integral\u5df2\u7ecf\u6709\u4e9b\u60f3\u6cd5 ?<\/p>\n

\u6df1\u8c37:\u4f60\u77e5\u9053\u7684,\u540c\u8c03\u662f\u67d0\u79cd\u6709\u76f8\u6d88\u4f5c\u7528\u4e0e\u8fb9\u754c\u7b97\u5b50(cancellation and boundaryoperator)\u7684\u89c2\u5ff5\u3002\u5728 path integral\u7684\u60c5\u5f62\u8981\u8ba9\u76f8\u6d88\u6709\u610f\u4e49,\u6211\u89c9\u5f97\u540c\u8c03\u4ee3\u6570 (homological al\u00adgebra)\u662f\u4e00\u79cd\u6bd4\u8f83\u7cfb\u7edf\u5316\u4e86\u89e3\u8fd9\u4e2a\u76f8\u6d88\u7684\u65b9\u6cd5 ,\u7269\u7406\u5b66\u5bb6\u901a\u5e38\u7528\u7eb8\u7b14\u8ba1\u7b97\u76f8\u6d88 ,\u8981\u7cfb\u7edf\u5316\u5730\u5904\u7406\u8fd9\u7c7b\u7684\u4e8b,\u5e94\u8be5\u662f\u6570\u5b66\u5bb6\u7684\u4efb\u52a1\u3002\u7269\u7406\u5b66\u5bb6\u5f88\u591a\u4e1c\u897f\u4ee5\u56fe\u6765\u8868\u793a,\u770b\u8d77\u6765\u4e0e\u62d3\u6734\u5b66\u5bb6\u7684\u56fe\u5f88\u76f8\u4f3c,\u6211\u4e0d\u77e5\u9053\u8fd9\u662f\u5426\u53ef\u80fd\u3002<\/p>\n

\u90d1:\u4f60\u53ef\u4ee5\u7565\u8fc7\u5206\u6790?<\/p>\n

\u6df1\u8c37:\u6211\u60f3\u8fd9\u90e8\u5206\u5fc5\u987b\u8981\u52a0\u8fdb\u53bb\u3002\u5206\u6790\u5e94\u8be5\u4e00\u76f4\u90fd\u5728\u90a3\u513f,\u4e3e\u4f8b\u6765\u8bf4,\u6709\u65f6\u5019\u62d3\u6734\u5b66\u5bb6\u63d0\u51fa\u601d\u8003\u7684\u65b9\u6cd5\u3002\u901a\u5e38\u4e00\u4e2a\u7b97\u5b50\u6709\u79bb\u6563\u7684\u9891\u8c31 (discrete spectrum),\u4f46\u5b9e\u9645\u4e0a\u7269\u7406\u662f\u8fde\u7eed\u9891\u8c31,\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\u5fc5\u987b\u5c06\u4ee3\u6570\u7684\u4e1c\u897f\u4e0e\u6cdb\u51fd\u5206\u6790\u7ed3\u5408\u3002\u6211\u60f3\u8bf4\u7684\u662f C*-algebra\u6216\u6cdb\u51fd\u5206\u6790
\n14\u8bd1\u6ce8 : Hermann Minkowski (1864-1909),\u5fb7\u56fd\u6570\u5b66\u5bb6 ,\u72b9\u592a\u4eba ,\u56db\u7ef4\u65f6\u7a7a\u7406\u8bba\u7684\u521b\u7acb\u8005\u3002 1907\u5e74, Minkowski\u8ba4\u8bc6\u5230\u53ef\u4ee5\u7528\u975e\u6b27\u7a7a\u95f4\u6765\u63cf\u8ff0\u52b3\u4ed1\u5179\u548c\u7231\u56e0\u65af\u5766\u7684\u5de5\u4f5c,\u5c06\u8fc7\u53bb\u88ab\u8ba4\u4e3a\u662f\u72ec\u7acb\u7684\u65f6\u95f4\u548c\u7a7a\u95f4\u7ed3\u5408\u5230\u4e00\u4e2a\u56db\u7ef4\u7684\u65f6\u7a7a\u7ed3\u6784\u4e2d,\u5373 Minkowski\u65f6\u7a7a\u3002\u95f5\u8003\u65af\u57fa\u65f6\u7a7a\u4e3a\u5e7f\u4e49\u76f8\u5bf9\u8bba\u7684\u5efa\u7acb\u63d0\u4f9b\u4e86\u6846\u67b6\u3002
\n15\u8bd1\u6ce8 : John von Neumann (1903-1957),\u51fa\u751f\u4e8e\u5308\u7259\u5229\u7684\u7f8e\u56fd\u7c4d\u72b9\u592a\u4eba\u6570\u5b66\u5bb6 ,\u73b0\u4ee3\u8ba1\u7b97\u673a\u521b\u59cb\u4eba\u4e4b\u4e00\u3002\u4ed6\u5728\u8ba1\u7b97\u673a\u79d1\u5b66\u3001\u7ecf\u6d4e\u3001\u7269\u7406\u5b66\u4e2d\u7684\u91cf\u5b50\u529b\u5b66\u53ca\u51e0\u4e4e\u6240\u6709\u6570\u5b66\u9886\u57df\u90fd\u4f5c\u8fc7\u91cd\u5927\u8d21\u732e\u3002
\n16\u8bd1\u6ce8 : James Glimm(1934-),\u7f8e\u56fd\u6570\u5b66\u5bb6 ,\u5728 C*-algebra,\u9707\u6ce2\u7406\u8bba,\u91cf\u5b50\u573a\u8bba,\u79d1\u5b66\u8ba1\u7b97\u7b49\u6570\u5b66\u79d1\u5b66\u7684\u6838\u5fc3\u9886\u57df,\u6709\u5f00\u521b\u6027\u7684\u91cd\u8981\u8d21\u732e\u3002
\n17\u8bd1\u6ce8 : Arthur Ja\ufb00e(1937-),\u7f8e\u56fd\u6570\u5b66\u7269\u7406\u5b66\u5bb6 ,\u4e0e James Glimm\u5bf9\u6240\u8c13 constructive quantum \ufb01eld theory\u505a\u4e86\u5960\u57fa\u7684\u5de5\u4f5c\u3002
\n18\u8bd1\u6ce8 : James Glimm\u6559\u6388\u7684\u4e13\u8bbf\u520a\u8f7d\u4e8e\u6570\u5b66\u4f20\u64ad, 31\u5377,4\u671f\u3002
\n19\u8bd1\u6ce8 : Alain Connes,\u6cd5\u56fd\u6570\u5b66\u5bb6 ,\u4e3b\u8981\u4ece\u4e8b\u7b97\u5b50\u4ee3\u6570\u3001\u975e\u4ea4\u6362\u51e0\u4f55\u7b49\u7684\u7814\u7a76, 1982\u5e74\u83b7\u5f97 Fields Medal\u3002
\n<\/p>\n

\u7528\u5230\u7684\u662f\u5f88\u57fa\u672c\u7684\u4ee3\u6570,\u4ece\u672a\u7528\u5230 (\u540c\u8c03)\u8fd9\u79cd\u9ad8\u5ea6\u53d1\u5c55\u7684\u4ee3\u6570,\u6211\u4e0d\u77e5\u9053\u8fd9\u6837\u505a\u662f\u5426\u6709\u5e0c\u671b\u3002<\/p>\n

\u5218:\u542c\u8d77\u6765\u5f88\u6709\u610f\u601d\u3002<\/p>\n

\u6df1\u8c37:\u5982\u679c\u80fd\u6210\u529f\u7684\u8bdd\u3002<\/p>\n

\u5218:\u4f46\u9996\u5148\u4f60\u81ea\u5df1\u8981\u611f\u5230\u5174\u594b\u3002<\/p>\n

\u6df1\u8c37:\u957f\u4e45\u4ee5\u6765\u8fd9\u4e9b\u60f3\u6cd5\u4e00\u76f4\u5728\u6211\u5fc3\u4e2d,\u4f46\u8fd9\u8fd8\u662f\u5f88\u9065\u8fdc\u7684\u4e8b\u3002<\/p>\n

\u5218:\u91cf\u5b50\u573a\u8bba\u4e00\u76f4\u6709\u65e0\u9650 (in\ufb01nity)\u8fd9\u4e8b\u8981\u594b\u529b\u9762\u5bf9\u3002<\/p>\n

\u90d1:\u4f60\u5982\u4f55\u5e73\u8861\u5bb6\u5ead\u751f\u6d3b\u4e0e\u5de5\u4f5c?\u4f60\u63d0\u5230\u4e60\u60ef\u5728\u665a\u4e0a\u5de5\u4f5c\u3002<\/p>\n

\u6df1\u8c37:\u4e8b\u5b9e\u4e0a ,\u901a\u5e38\u5728\u59bb\u5b50\u3001\u5c0f\u5b69\u90fd\u7761\u4e86\u4ee5\u540e,\u5927\u7ea611\u70b9\u5f00\u59cb\u5de5\u4f5c\u5230\u7b2c\u4e8c\u5929\u65e9\u4e0a\u624d\u4f11\u606f\u3002<\/p>\n

\u5218:\u4f60\u592a\u592a\u77e5\u9053\u4f60\u665a\u4e0a\u5de5\u4f5c,\u5bf9\u5417?<\/p>\n

\u6df1\u8c37:\u55ef,\u5979\u77e5\u9053\u6211\u534a\u591c\u5de5\u4f5c\u3002<\/p>\n

\u5218:\u90a3\u767d\u5929\u4e0a\u73ed\u7684\u5de5\u4f5c\u5462?<\/p>\n

\u6df1\u8c37:\u767d\u5929\u7684\u5de5\u4f5c\u554a,\u6211\u7684\u56f0\u6270\u662f\u6709\u8bb8\u591a\u6587\u4e66\u4f5c\u4e1a\u8981\u5904\u7406 (paper work),\u4f60\u5e94\u8be5\u4e5f\u6709\u7c7b\u4f3c\u7684\u95ee\u9898,\u65e5\u672c\u73b0\u5728\u8fd9\u6837\u7684\u4e8b\u6108\u6765\u6108\u591a\u3002<\/p>\n

\u5218:\u662f\u554a,\u6211\u4e5f\u542c\u8bf4\u8fc7 ,\u600e\u4e48\u4f1a\u8fd9\u6837\u5462?\u56e0\u4e3a\u6709\u8bb8\u591a\u884c\u653f\u65b9\u9762\u7684\u6587\u4ef6\u5417?<\/p>\n

\u6df1\u8c37:\u6211\u4eec\u7ecf\u5e38\u9700\u8981\u5199\u8bb8\u591a\u4e1c\u897f,\u8981\u62ff\u5230\u7ecf\u8d39\u9700\u8981\u5199\u4e00\u8fed\u539a\u539a\u7684\u8ba1\u5212,\u8ba1\u5212\u7ed3\u675f\u540e\u53c8\u8981\u5199\u6267\u884c\u62a5\u544a\u3002\u6240\u4ee5\u82b1\u5728\u8bf4\u660e\u4e0a\u7684\u65f6\u95f4\u6bd4\u771f\u6b63\u6267\u884c\u8ba1\u5212\u7684\u65f6\u95f4\u8fd8\u591a\u3002\u6211\u4eec\u5f97\u8981\u8bc1\u660e\u6240\u505a\u7684\u5de5\u4f5c(\u503c\u5f97\u5f97\u5230\u7ecf\u8d39\u7684\u8d44\u52a9),\u8981\u62a5\u544a\u4eca\u5e74\u505a\u4e86\u751a\u4e48\u7814\u7a76,\u6709\u591a\u5c11\u5b66\u751f\u79cd\u79cd\u3002<\/p>\n

\u6c5f:\u6211\u60f3\u95ee\u4e00\u4e2a\u5236\u5f0f\u7684\u95ee\u9898,\u4f60\u505a\u7814\u7a76\u5361\u4f4f\u7684\u65f6\u5019,\u600e\u4e48\u529e\u5462?\u90d1:\u4f60\u5361\u4f4f\u65f6,\u662f\u7528\u4ec0\u4e48\u6001\u5ea6\u9762\u5bf9?<\/p>\n

\u6df1\u8c37:\u559d\u9152\u89e3\u95f7\u5427,\u600e\u4e48?<\/p>\n

\u5218:\u4ed6\u7814\u7a76\u4ece\u4e0d\u4f1a\u5361\u4f4f\u3002<\/p>\n

\u6df1\u8c37:\u4e0d!\u4e0d!\u4f1a\u88ab\u5361\u4f4f!(\u7b11)\u3002\u4e0d\u8fc7\u5904\u7406\u884c\u653f\u6587\u4ef6\u6700\u59a8\u788d\u505a\u6570\u5b66\u3002\u6240\u4ee5\u6211\u7814\u7a76\u5361\u4f4f\u65f6,\u5f88\u5bb9\u6613\u529e,\u5c31\u53bb\u5904\u7406\u884c\u653f\u6587\u4ef6\u3002\u53ea\u662f,\u4e00\u65e6\u4ecb\u5165\u884c\u653f\u7684\u4e8b,\u5c31\u6015\u56de\u4e0d\u4e86\u7814\u7a76\u4e86\u3002<\/p>\n

\u5218:\u8bf4\u771f\u7684 ,\u5c31\u4f60\u7684\u7eaa\u5f55,\u4f60\u66fe\u5361\u4f4f\u8fc7\u591a\u4e45\u624d\u53c8\u80fd\u7ee7\u7eed\u7814\u7a76?<\/p>\n

\u6df1\u8c37:\u4f60\u4e5f\u77e5\u9053,\u6709\u4e9b\u65f6\u5019\u8bd5\u4e86\u4f46\u4ece\u672a\u6210\u529f,\u4e5f\u8bb8\u8fd9\u4e0d\u7b97\u3002\u4e0d\u8fc7,\u4e5f\u6709\u4e9b\u9898\u76ee,\u6211\u8bd5\u4e86\u5341\u51e0\u5e74\u4e5f\u8fd8\u672a\u6210\u529f\u3002\u6211\u4e0d\u80fd\u4e00\u76f4\u628a\u65f6\u95f4\u7cbe\u529b\u96c6\u4e2d\u5728\u8fd9\u7c7b\u7684\u95ee\u9898\u4e0a\u3002\u6709\u4e9b\u95ee\u9898,\u5148\u5f00\u4e86\u5934,\u8fc7\u51e0\u4e2a\u6708\u4ee5\u540e\u518d\u56de\u5934\u7ee7\u7eed\u3002<\/p>\n

\u5218:\u4f46\u6709\u4e9b\u95ee\u9898\u5b9e\u9645\u4e0a\u662f\u653e\u5728\u8111\u5b50\u91cc\u5341\u5e74,\u4e00\u76f4\u90fd\u5728\u60f3\u7684\u3002<\/p>\n

\u6df1\u8c37:\u662f\u7684 ,\u6bd4\u65b9\u8bf4\u6211\u4eec\u56db\u4e2a\u4eba (\u6307 Fukaya, Ohta, Ono, Oh)\u5408\u5199\u4e86\u4e00\u672c\u4e66 20 ,\u6211\u4eec\u8bc1\u660e Lagrangian Floer homology\u7684\u5b58\u5728\u3002\u5728\u8fd9\u4e2a\u8fc7\u7a0b\u4e2d,\u6211\u9047\u5230\u4e86\u4e9b\u9ebb\u70e6,\u6240\u4ee5\u6211\u8bd5\u4e86\u591a<\/p>\n

20\u8bd1\u6ce8 : K. Fukaya, H. Ohta, K. Ono, Y-G. Oh, Lagrangian intersection Floer theory -anomaly and obstruction, In preparation.<\/p>\n

<\/p>\n

\u79cd\u65b9\u6cd5\u60f3\u628a\u95ee\u9898\u6392\u9664,\u82b1\u4e86\u4e24\u4e2a\u6708\u7684\u65f6\u95f4,\u540e\u6765\u6211\u8ba4\u4e3a\u4e0d\u8be5\u662f\u8fd9\u6837,\u51b3\u5b9a\u653e\u5f03\u3002\u6211\u505c\u4e0b\u811a\u6b65,\u518d\u52a0\u4e9b\u6761\u4ef6\u3002\u5728\u90a3\u4e24\u4e2a\u6708\u4e2d,\u6211\u9664\u4e86\u8fd9\u4ef6\u4e8b\u60c5\u6ca1\u505a\u4efb\u4f55\u5176\u5b83\u6570\u5b66\u3002\u4e8b\u5b9e\u4e0a ,\u5f53\u65f6\u6211\u592a\u592a\u6000\u5b55,\u6211\u5e38\u5230\u533b\u9662 ,\u4f46\u662f\u2022\u2022\u2022<\/p>\n

\u5218:\u4ecd\u7136\u5728\u60f3\u8fd9\u4e2a\u95ee\u9898?<\/p>\n

\u6df1\u8c37:\u662f\u3002(\u7b11)<\/p>\n

\u5218:\u6240\u4ee5\u73b0\u5728\u4f60\u5df2\u7ecf\u5f00\u59cb\u7740\u624b\u5b9e\u73b0\u4f60\u7684\u68a6\u60f3,\u62bd\u51fa\u65f6\u95f4\u6765\u601d\u8003\u91cf\u5b50\u573a\u8bba\u5417?<\/p>\n

\u6df1\u8c37:\u8fd9\u662f\u975e\u5e38\u56f0\u96be\u7684,\u4e5f\u8bb8\u8fd8\u9700\u8981\u5b66\u4e9b\u4e1c\u897f,\u6211\u89c9\u5f97\u8be5\u770b\u4e9b Ja\ufb00e\u548c\u5176\u4ed6\u4eba\u7684\u8bba\u6587\u3002<\/p>\n

\u5218:\u4f46\u4f60\u771f\u7684\u60f3\u505a?<\/p>\n

\u6df1\u8c37:\u4e5f\u8bb8\u5c06\u6765\u5427,\u4e5f\u8bb8\u6211\u8981\u5148\u628a\u505a\u8fd9\u4e8b\u7684\u884c\u653f\u5de5\u4f5c (paper work)\u5904\u7406\u597d\u3002<\/p>\n

\u5218:\u6709\u4e9b\u4eba\u56e0\u4e3a\u9700\u8981\u6709\u8868\u73b0\u6216\u662f\u6709\u6210\u5c31\u7684\u538b\u529b,\u6240\u4ee5\u4e0d\u80fd\u505a\u957f\u65f6\u95f4\u624d\u53ef\u80fd\u505a\u51fa\u6765\u7684\u96be\u9898\u3002\u4f60\u5e94\u8be5\u6ca1\u6709\u8fd9\u79cd\u987e\u8651\u662f\u5427,\u4f60\u53ef\u4ee5\u968f\u5fc3\u6240\u6b32\u505a\u60f3\u505a\u7684\u95ee\u9898?<\/p>\n

\u6df1\u8c37:\u4e8b\u5b9e\u4e0a ,\u67d0\u79cd\u7a0b\u5ea6\u6765\u8bf4\u6211\u4eec\u51e0\u4e4e\u8981\u5b8c\u6210\u4e00\u4e2a\u5341\u5e74\u8ba1\u5212,\u90a3\u662f Floer Theory,\u63a5\u4e0b\u6765\u6211\u4eec\u9700\u8981\u540c\u65f6\u505a\u4e9b\u8ba1\u7b97\u3002\u6211\u4eec\u5df2\u7ecf\u5ba3\u5e03\u4e865\u30016\u7bc7\u6b63\u5728\u5199\u7684\u8bba\u6587\u3002\u5927\u6982\u9700\u8981\u51e0\u5e74\u624d\u80fd\u5168\u90e8\u5199\u597d\u3002\u5728\u5199\u7684\u65f6\u5019\u6211\u5e0c\u671b\u80fd\u5c31\u8fd9\u4e2a\u65b9\u5411\u627e\u5230\u4e00\u4e9b\u4e1c\u897f,\u6240\u4ee5\u4e0d\u77e5\u9053\u751a\u4e48\u65f6\u5019\u624d\u4f1a\u7ed3\u675f\u8fd9\u4e2a\u8ba1\u5212\u3002\u53e6\u4e00\u65b9\u9762,\u8fd9\u4e5f\u662f\u4e2a\u503c\u5f97\u7ee7\u7eed\u7684\u8ba1\u5212,\u6240\u4ee5\u76ee\u524d\u6ca1\u6709\u90a3\u4e48\u591a\u7684\u81ea\u7531\u53ef\u4ee5\u6362\u505a\u5176\u5b83\u9898\u76ee\u3002\u4e5f\u8bb8\u5728\u9898\u76ee\u4ecd\u7136\u6709\u8da3\u7684\u65f6\u5019\u5c31\u8fdb\u5165\u6bd4\u8f83\u597d,\u5982\u679c\u6ca1\u6709\u5269\u4e0b\u591a\u5c11\u6709\u8da3\u7684\u4e1c\u897f\u624d\u8fdb\u5165,\u90a3\u65f6\u53ef\u80fd\u5c31\u6ca1\u6709\u8db3\u591f\u7684\u80fd\u529b\u53bb\u8fdb\u884c ,\u8fd9\u5c31\u4e0d\u5927\u597d\u4e86\u3002<\/p>\n

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\u6df1\u8c37:\u6709\u4ec0\u4e48\u574f\u5904?<\/p>\n

\u5218:\u5c31\u662f\u4e0d\u4f1a\u6709\u673a\u4f1a\u6210\u4e3a\u7f8e\u56fd\u4eba\u8bf4\u7684\u201dProfessorial\u201d\u7684\u5b66\u8005,\u6709\u6e0a\u535a\u7684\u77e5\u8bc6,\u80fd\u591f\u5f15\u9886\u8de8\u9886\u57df\u7814\u7a76,\u5e76\u4e14\u80fd\u4e3a\u4e0b\u4e00\u4ee3\u7684\u517b\u6210\u8425\u9020\u66f4\u591a\u5143\u7684\u6587\u5316\u73af\u5883\u3002<\/p>\n

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\u5218:\u662f\u554a,\u6211\u4eec\u6570\u5b66\u7814\u7a76\u6210\u719f\u7684\u8fdb\u7a0b\u5ef6\u957f\u4e86,\u611f\u5230\u6c38\u8fdc\u50cf\u662f\u4e2a\u65b0\u9c9c\u4eba\u3002\u6211\u5f88\u9ad8\u5174\u95ee\u4e86\u8fd9\u4e2a\u95ee\u9898,\u66f4\u9ad8\u5174\u542c\u5230\u8fd9\u6837\u7684\u56de\u7b54\u3002\u7ecf\u8fc7 5\u5929\u7684\u4f1a\u8bae,\u4f60\u4e00\u5b9a\u5f88\u7d2f\u4e86,\u4f46\u662f\u6211\u770b\u5f97\u51fa\u6765 ,\u4f60\u8fd8\u662f\u6d3b\u529b\u5145\u6c9b\u3002<\/p>\n

\u6df1\u8c37:\u8c08\u6570\u5b66\u6c38\u8fdc\u662f\u4e2a\u4e50\u8da3\u3002<\/p>\n

\u5218:\u5bf9!\u4e5f\u8bb8\u6211\u4eec\u53ef\u4ee5\u5728\u6b64\u6253\u4f4f\u3002\u4f60\u6709\u8bb8\u591a\u6d1e\u89c1,\u4ee4\u4eba\u8033\u76ee\u4e00\u65b0\u3002\u8c22\u8c22\u4f60\u3002<\/p>\n

—–\u672c\u6587\u8bbf\u95ee\u8005\u5218\u592a\u5e73\u3001\u90d1\u65e5\u65b0\u4efb\u804c\u4e2d\u592e\u7814\u7a76\u9662\u6570\u5b66\u6240,\u6c5f\u5b5f\u84c9\u4efb\u6559\u6210\u529f\u5927\u5b66\u6570\u5b66\u7cfb,\u6574\u7406\u8005\u9648\u4e3d\u4f0d\u4e3a\u4e2d\u592e\u7814\u7a76\u9662\u6570\u5b66\u6240\u52a9\u7406\u2014<\/p>\n","protected":false},"excerpt":{"rendered":"

Kenjin Fukaya \u6709\u670b\u81ea\u8fdc\u65b9\u6765\u4e00\u4e00\u4e13\u8bbf\u6df1\u8c37 \u8d24\u6cbb (Kenji Fuk …<\/p>\n

\u6709\u670b\u81ea\u9060\u65b9\u4f86\u4e00\u4e00\u5c08\u8a2a\u6df1\u8c37\u8ce2\u6cbb<\/span> \u9605\u8bfb\u66f4\u591a »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[136,78,748],"class_list":["post-1592","post","type-post","status-publish","format-standard","hentry","category-net","tag-136","tag-78","tag-748"],"_links":{"self":[{"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts\/1592","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1592"}],"version-history":[{"count":0,"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts\/1592\/revisions"}],"wp:attachment":[{"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1592"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1592"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1592"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}