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\n\u4ee5\u65e0\u7aef\u653b\u51fb\u3002\u4e3a\u6b64\u4ed6\u66fe\u653b\u51fb\u8fc7\u9648\u7701\u8eab\u6559\u6388\uff0c\u5e76\u5728\u4e0d\u540c\u573a\u5408\u8d2c\u4f4e\u5434\u6587\u4fca\u5148\u751f\u3002\u8fd1\u5e74\u6765\uff0c\u968f\u7740
\n\u7530\u521a\u6559\u6388\u5728\u56fd\u9645\u4e0a\u7684\u5a01\u671b\u4e0e\u65e5\u4ff1\u589e\uff08\u7530\u521a\u662fICM2002\u7a0b\u5e8f\u59d4\u5458\u4f1a\u6210\u5458\uff0c\u4ed6\u4e5f\u5e94IMU\u9080\u8bf7\u53c2\u52a0
\n\u4e86ICM2006\u7684\u7b79\u5907\u5de5\u4f5c\uff09\u548c\u5728\u56fd\u5185\u5f71\u54cd\u8d8a\u6765\u8d8a\u5927\uff0c\u4e18\u611f\u5230\u7530\u662f\u5bf9\u4ed6\u7684\u9738\u4e3b\u5730\u4f4d\u7684\u6700\u4e25\u91cd\u7684
\n\u5a01\u80c1\uff0c\u56e0\u800c\u5904\u5fc3\u79ef\u8651\u548c\u4e0d\u9057\u4f59\u529b\u5730\u5bf9\u7530\u521a\u6559\u6388\u52a0\u4ee5\u731b\u70c8\u653b\u51fb\uff0c\u540c\u65f6\u4e5f\u5bf9\u62b5\u5236\u4ed6\u7684\u9738\u6743\u7684\u5317
\n\u4eac\u5927\u5b66\u731b\u70c8\u653b\u51fb\u3002\u6211\u4eec\u8981\u63d0\u9192\u4e18\u6210\u6850\u5148\u751f\uff1a\u5728\u4eca\u5929\u6c11\u4e3b\u5df2\u6210\u4e3a\u4e0d\u53ef\u6297\u62d2\u7684\u6f6e\u6d41\uff0c\u4efb\u4f55\u5e7b\u60f3
\n\u201c\u79f0\u738b\u79f0\u9738\u201d\u7684\u4eba\u90fd\u4e0d\u53ef\u80fd\u53d6\u5f97\u6210\u529f\u3002\u3000<\/p>\n
\u4e18\u4e00\u65b9\u9762\u5bf9\u6743\u529b\u6781\u529b\u8ffd\u6c42\uff08\u4ed6\u66fe\u591a\u6b21\u7ade\u9009\u9999\u6e2f\u67d0\u4e9b\u5927\u5b66\u6821\u957f\u7684\u4f4d\u5b50\uff0c\u4f46\u5747\u672a\u6210\u529f\uff1b\u636e\u8bf4\u66fe
\n\u56e0\u4ed6\u7684\u5984\u81ea\u5c0a\u5927\u800c\u88ab\u9074\u9009\u59d4\u5458\u5632\u7b11\u4e3a\u201c\u6570\u5b66\u5bb6IQ\u592a\u4f4e\u201d\uff0c\u8fde\u7d2f\u4e86\u5168\u4f53\u6570\u5b66\u5bb6\uff09\uff0c\u53e6\u4e00\u65b9\u9762
\n\u53c8\u5bf9\u63e1\u6709\u6743\u52bf\u7684\u4eba\u5351\u8eac\u5c48\u819d\u3002\u53ea\u4e3e\u4e00\u4e2a\u4f8b\u5b50\u3002\u4e2d\u56fd\u79d1\u6280\u5927\u5b66\u6210\u7acb\u4e0a\u6d77\u7814\u7a76\u751f\u9662\u7684\u65f6\u5019\uff0c\u66fe
\n\u9080\u8bf7\u4e18\u62c5\u4efb\u9886\u5bfc\u804c\u52a1\uff0c\u4e18\u6b23\u7136\u5e94\u5141\u3002\u4e0d\u6599\u56fd\u5185\u67d0\u9996\u957f\u5bf9\u6b64\u6301\u53cd\u5bf9\u6001\u5ea6\uff0c\u4e18\u542c\u8bf4\u540e\u7acb\u5373\u6539\u53d8
\n\u4e3b\u610f\uff0c\u5426\u8ba4\u4ed6\u66fe\u7b54\u5e94\u8fc7\u8981\u62c5\u4efb\u9886\u5bfc\u7684\u4e8b\u3002<\/p>\n
3\uff0e\u6076\u52a3\u7684\u5b66\u9738\u4f5c\u98ce\u3002<\/p>\n
1997\u5e74\u590f\uff0c\u6668\u5174\u4e2d\u5fc3\u5f00\u59cb\u7b2c\u4e00\u6b21\u6d3b\u52a8\u3002\u5f53\u65f6\u6070\u9022Hamilton\u5199\u4e86\u51e0\u7bc7Ricci\u6d41\u7684\u6587\u7ae0\uff0c\u4e18\u4ee5
\n\u4e3a\u4ed6\u68a6\u5bd0\u4ee5\u6c42\u60f3\u8981\u89e3\u51b3\u7684Poincare\u731c\u60f3\uff0c\u53ef\u4ee5\u7528Hamilton\u7684\u65b9\u6cd5\u6765\u505a\uff0c\u5e76\u4e14\u5173\u952e\u662f\u5efa\u7acb\u4e00
\n\u4e2aHarnack\u4e0d\u7b49\u5f0f\u3002\u4e8e\u662f\uff0c\u4e00\u65b9\u9762\u4ed6\u672c\u4eba\u7d27\u8ffdHamilton\u4f01\u56fe\u5b9e\u73b0\u4ed6\u7684\u68a6\u60f3\uff0c\u53e6\u4e00\u65b9\u9762\u4ed6\u6307
\n\u793a\u5317\u4eac\uff08\u6668\u5174\u4e2d\u5fc3\uff09\uff0c\u9999\u6e2f\uff08\u4e2d\u6587\u5927\u5b66\uff09\uff0c\u53f0\u6e7e\uff08\u9ad8\u7b49\u7406\u8bba\u4e2d\u5fc3\uff09\u7684\u6709\u5173\u7814\u7a76\u5c0f\u7ec4\u90fd\u8981\u7814
\n\u7a76Ricci\u6d41\u3002\u5176\u5b9e\u6570\u5b66\u548c\u5176\u4ed6\u79d1\u5b66\u4e00\u6837\uff0c\u6709\u5176\u81ea\u8eab\u7684\u53d1\u5c55\u89c4\u5f8b\uff0c\u4f01\u56fe\u901a\u8fc7\u6743\u5a01\u6307\u6325\u548c\u63a7\u5236
\n\u6765\u53d6\u5f97\u6210\u679c\u6ce8\u5b9a\u8981\u5931\u8d25\u3002\u636e\u5317\u4eac\u5c0f\u7ec4\u7684\u4eba\u4ecb\u7ecd\uff0c\u4ed6\u4eec\u5728\u7814\u8bfbHamilton\u6587\u7ae0\u8fc7\u7a0b\u4e2d\u53d1\u73b0\uff1a\u5176
\n\u6587\u7ae0\u542b\u6709\u4e00\u4e9b\u5173\u952e\u6027\u7684\u758f\u6f0f\uff08gaps\uff09\u3002\u7531\u4e8e\u65e0\u6cd5\u514b\u670d\u8fd9\u4e9b\u758f\u6f0f\uff0c\u8be5\u5c0f\u7ec4\u6682\u505c\u4e86\u4e00\u4e0b\uff0c\u7528\u4e86
\n\u4e24\u6bb5\u65f6\u95f4\u53bb\u8bfb\u6797\u82b3\u534e\u7684\u4e00\u7bc7\u91cd\u8981\u6587\u7ae0\uff08\u540e\u6765\u53d1\u8868\u5728Annals of Math.\uff09\u3002\u8fd9\u672c\u6765\u662f\u5f88\u6b63\u5e38
\n\u7684\uff0c\u5c82\u6599\u4e18\u5728\u5317\u4eac\u7684\u603b\u7ba1\u628a\u6b64\u4e8b\u6253\u5c0f\u62a5\u544a\u7ed9\u8fdc\u5728\u7f8e\u56fd\u7684\u4e18\uff0c\u56e0\u800c\u624d\u6709\u540e\u6765\u4e18\u51e0\u6b21\u6b6a\u66f2\u4e8b\u5b9e
\n\u653b\u51fb\u5317\u4eac\u5c0f\u7ec4\u9886\u5bfc\u4eba\u7684\u4e8b\u3002\u73b0\u5df2\u8bc1\u5b9e\uff0cHamilton\u7684\u6587\u7ae0\u786e\u5b9e\u6709\u8bef\uff0c\u6700\u8fd1\u5df2\u88ab\u4eba\u7528Perelman
\n\u7684\u601d\u60f3\u52a0\u4ee5\u66f4\u6b63\uff1b\u800c\u4e18\u7684\u60f3\u6cd5\u4e5f\u6ca1\u6210\u529f\uff0c\u662f\u4fc4\u56fd\u6570\u5b66\u5bb6Perelman\u53e6\u8f9f\u8e4a\u5f84\u624d\u53d6\u5f97\u4e86\u6210\u529f\u3002
\n\u62ff\u81ea\u5df1\u4e0d\u6210\u529f\u7684\u7ecf\u5386\u6765\u5439\u5618\uff0c\u8bf4\u81ea\u5df1\u6709\u201c\u5148\u89c1\u4e4b\u660e\u201d\uff0c\u540c\u65f6\u5bf9\u4ed6\u4eba\u52a0\u4ee5\u83ab\u987b\u6709\u7684\u653b\u51fb\uff0c\u5b9e
\n\u5728\u662f\u5f88\u4e0d\u5149\u5f69\u7684\u3002<\/p>\n
\u6700\u8fd1\uff0c\u4e18\u5728\u4ed6\u5bf9\u5a92\u4f53\u7684\u8c08\u8bdd\u4e2d\u591a\u6b21\u9020\u8c23\u4e2d\u4f24\uff0c\u79f0\u7530\u521a\uff08\u548c\u53e6\u4e00\u4f4d\u4e2d\u56fd\u5b66\u8005\u5408\u4f5c\uff09\u5728\u4e00\u7bc7\u6587
\n\u7ae0\u4e2d\u527d\u7a83\u4e86\u4ed6\u540c\u4e00\u4f4d\u5fb7\u56fd\u6570\u5b66\u5bb6\u7684\u5de5\u4f5c\u3002\u6240\u8c13\u201c\u527d\u7a83\u201d\u7684\u5de5\u4f5c\uff0c\u662f\u6307\u7406\u8bba\u7269\u7406\u4e2d\u6240\u8c13
\n\u201cADM\u8d28\u91cf\u201d\u662f\u5426\u6709\u4e0d\u4f9d\u8d56\u4e8e\u5750\u6807\u7cfb\u7684\u5b9a\u4e49\u3002\u8fd9\u4e2a\u95ee\u9898\u662f\u7269\u7406\u5b66\u5bb6\u63d0\u51fa\u6765\u7684\uff0c\u4e18\u53ca\u5176\u5408\u4f5c
\n\u8005\u5e76\u6ca1\u80fd\u5b8c\u5168\u89e3\u51b3\u5b83\uff0c\u800c\u662f\u5728\u4e00\u5b9a\u6761\u4ef6\u4e0b\u5f97\u5230\u4e86\u90e8\u5206\u7ed3\u679c\u3002\u4ed6\u4eec\u5728\u6587\u7ae0\u4e2d\u8fd8\u628a\u8fd9\u4e2a\u95ee\u9898\u5f53
\n\u4f5c\u516c\u5f00\u95ee\u9898\u63d0\u51fa\u6765\uff0c\u5e76\u627f\u8ba4\u4ed6\u4eec\u7684\u65b9\u6cd5\u5df2\u8fbe\u5230\u6781\u9650\uff0c\u65e0\u6cd5\u8fdb\u4e00\u6b65\u89e3\u51b3\u5168\u90e8\u95ee\u9898\u3002\uff08\u89c1
\np.301, Invent. Math. Vol. 124\uff09\u73b0\u5728\uff0c\u7530\u521a\u53ca\u5176\u5408\u4f5c\u8005\u7528\u65b0\u7684\u5de7\u5999\u7684\u65b9\u6cd5\u5b8c\u5168\u89e3\u51b3\u4e86
\n\u8fd9\u4e00\u95ee\u9898\uff0c\u4efb\u4f55\u6709\u826f\u77e5\ufe51\u6709\u5224\u65ad\u529b\u7684\u6570\u5b66\u5bb6\u90fd\u770b\u4e0d\u51fa\u7530\u521a\u53ca\u5176\u5408\u4f5c\u8005\u6709\u4efb\u4f55\u201c\u527d\u7a83\u201d\uff0c\u800c
\n\u8bec\u8511\u4ed6\u4eec\u201c\u527d\u7a83\u201d\u7684\u4eba\u5fc5\u5b9a\u662f\u5fc3\u7406\u4e0d\u6b63\u5e38\u3002\u4e18\u7684\u4e0d\u6b63\u5e38\u5fc3\u7406\u662f\uff1a\u4ed6\u505a\u8fc7\u7684\u8fd9\u4e2a\u95ee\u9898\u5df2\u7ecf\u53d8
\n\u6210\u4e86\u4ed6\u7684\u79c1\u6709\u8d22\u4ea7\uff0c\u4efb\u4f55\u4eba\u8981\u6765\u7814\u7a76\u5fc5\u987b\u6709\u4ed6\u7684\u8bb8\u53ef\uff0c\u5426\u5219\u5c31\u662f\u201c\u527d\u7a83\u201d\u3002\u5176\u5b66\u672f\u9738\u9053\u7684
\n\u9762\u76ee\u66b4\u9732\u65e0\u9057\u3002[\u5185\u884c\u7684\u4eba\u53ef\u4ee5\u6bd4\u8f83\u7530\u7684\u6587\u7ae0\uff1amath.DG\/0506005 \u548c\u4e18\u7684\u6587\u7ae0\uff0c\u4ee5\u5f97\u51fa\u81ea
\n\u5df1\u7684\u7ed3\u8bba\u3002]<\/p>\n
\u4e00\u822c\u4eba\u4ee5\u4e3a\u4e18\u6210\u6850\u5728\u56fd\u5185\u7684\u5f71\u54cd\u4ee5\u6d59\u6c5f\u5927\u5b66\u4e3a\u6700\uff0c\u5176\u5b9e\u4ed6\u5728\u4e2d\u79d1\u9662\u7684\u5f71\u54cd\u66f4\u5927\u30022002\u5e74\uff0c
\n\u4e2d\u79d1\u9662\u6570\u5b66\u4e0e\u7cfb\u7edf\u79d1\u5b66\u7814\u7a76\u9662\u9886\u5bfc\u73ed\u5b50\u5373\u5c06\u6362\u5c4a\uff0c\u9662\u957f\u5019\u9009\u4eba\u4e2d\u4ee5\u521a\u521a\u6210\u529f\u5730\u9886\u5bfc\u4e86
\nICM2002\u7b79\u5907\u548c\u53ec\u5f00\u7684\u67d0\u9662\u58eb\u7684\u547c\u58f0\u6700\u9ad8\uff0c\u51e0\u4e4e\u662f\u552f\u4e00\u7684\u5019\u9009\u4eba\u3002\u4f46\u662f\u7531\u4e8e\u4ed6\u5728\u4e3e\u529e
\nICM2002\u7684\u8fc7\u7a0b\u4e2d\u56e0\u575a\u6301\u539f\u5219\u5f97\u7f6a\u4e86\u4e18\uff0c\u4e18\u575a\u51b3\u53cd\u5bf9\u4ed6\u505a\u4e0b\u4e00\u4efb\u9662\u957f\u3002\u4e3a\u6b64\uff0c\u4e18\u6307\u793a\u7814\u7a76
\n\u9662\u4e2d\u4e0e\u4ed6\u5173\u7cfb\u5bc6\u5207\u7684\u4e00\u4e9b\u9662\u58eb\uff0c\u5343\u65b9\u767e\u8ba1\u4e5f\u8981\u628a\u8be5\u9662\u58eb\u53cd\u6389\u3002\u8fd9\u4e9b\u9662\u58eb\u4e8e\u662f\u5171\u8d74\u79d1\u5b66\u9662\u9662
\n\u90e8\uff0c\u664b\u89c1\u9662\u957f\uff0c\u8868\u793a\u652f\u6301\u4e18\u7684\u53cd\u5bf9\u610f\u89c1\u3002\u8fd9\u4f4d\u5019\u9009\u4eba\u5c31\u8fd9\u6837\u88ab\u53cd\u4e86\u4e0b\u6765\u3002\u8fd9\u5b8c\u5168\u51fa\u4e4e\u7edd\u5927
\n\u591a\u6570\u4eba\u7684\u9884\u6599\u3002\u66ff\u4ee3\u7684\u5019\u9009\u4eba\u601d\u60f3\u4e0a\u4e5f\u6beb\u65e0\u51c6\u5907\uff0c\u8fdf\u8fdf\u4e0d\u80fd\u4e0b\u51b3\u5fc3\u63a5\u53d7\u8fd9\u4e2a\u9662\u957f\u7684\u91cd\u4efb\uff0c
\n\u81f4\u4f7f\u6362\u5c4a\u5de5\u4f5c\u63a8\u8fdf\u4e24\u4e2a\u6708\u624d\u5b8c\u6210\u3002<\/p>\n
4\uff0e\u5de7\u53d6\u8c6a\u593a\u7684\u5b66\u98ce\u3002<\/p>\n
\u5728\u4fc4\u56fd\u8457\u540d\u6570\u5b66\u5bb6V. I. Arnold\u7684\u4e00\u7bc7\u6587\u7ae0\u4e2d\u5199\u4e86\u4e00\u4e9b\u672c\u4e0d\u5fc5\u5199\u7684\u8bdd\uff0c\u89c1
\n\u201cMathematics: Frontiers and Perspectives\u201d\u7b2c409\u9875\u3002Arnold\u5199\u9053\uff1a\u201c\u76d6\u5c14\u82b3\u5fb7\u603b\u662f
\n\uff08\u6b63\u786e\u5730\uff09\u5f3a\u8c03\uff1a\u6570\u5b66\u5bb6\u4eec\u4ece\u6765\u4e0d\u6b23\u8d4f\u65b0\u601d\u60f3\uff0c\u5728\u6574\u4e2a\u767b\u5c71\u8fc7\u7a0b\u4e2d\u53ea\u6709\u767b\u4e0a\u9876\u5cf0\u7684\u90a3\u4e00\u6b65
\n\u624d\u7b97\u6570\u3002\u201d\u5728\u8fd9\u53e5\u8bdd\u540e\uff0cArnold\u52a0\u4e86\u4e00\u4e2a\u811a\u6ce8\uff1a\u201cM. M. Postnikov\u6709\u4e00\u4e2a\u66f4\u6fc0\u8fdb\u7684\u8bf4
\n\u6cd5\uff1a\u79d1\u5b66\u4ece\u6765\u4e0d\u63a5\u53d7\u65b0\u601d\u60f3\uff0c\u5b83\u540c\u65b0\u601d\u60f3\u4f5c\u6597\u4e89\u3002\u591a\u6570\u79d1\u5b66\u5bb6\u603b\u5728\u505a\u4e00\u4e9b\u5982\u540c\u9489\u9a6c\u638c\u7684\u5de5
\n\u4f5c\uff0c\u4ed6\u4eec\u81ea\u7136\u5bf9\u5927\u5ba2\u8f66\u6709\u4e0d\u597d\u7684\u770b\u6cd5\u3002\u89c1\u672c\u4e66\u4e2dS.-T. Yau\u5bf9\u4e8eGivental\u7406\u8bba\u7684\u5947\u602a\u7684\u6597
\n\u4e89\u3002\u201d\u8fd9\u91cc\u7684S.-T. Yau\u5c31\u662f\u4e18\u6210\u6850\u3002Arnold\u8fd9\u6bb5\u8bdd\u5f53\u7136\u662f\u6709\u7684\u800c\u53d1\u7684\uff0cGivental\u662f\u4ed6\u7684
\n\u5b66\u751f\uff0c\u800c\u4e18\u5f53\u65f6\u6b63\u5728\u4e0e\u4e4b\u4e89\u593a\u5173\u4e8e\u201c\u955c\u50cf\u5bf9\u79f0\u201d\u7684\u4e00\u4e2a\u7ed3\u679c\u7684\u4f18\u5148\u6743\u3002Givental\u7684\u6587\u7ae0\u53d1
\n\u8868\u5728\u5148\uff081996\uff09\uff0c\u4e18\u7b49\u4eba\u7684\u6587\u7ae0\u53d1\u8868\u5728\u540e\uff081997\uff09\u3002\u4f46\u4e18\u58f0\u79f0\uff08\u89c1\u8be5\u4e66\u7684382\u9875\uff09\uff1aManin
\n\u4e00\u4e2a\u9884\u5370\u672c\u4e2d\u66fe\u8bf4Givental\u7684\u8bba\u8bc1\u8fd8\u9700\u8981\u5b8c\u5584\uff0c\u56e0\u6b64\u4e18\u7b49\u4eba\u7684\u5de5\u4f5c\u662f\u7b2c\u4e00\u4e2a\u5b8c\u6574\u7684\u8bc1\u660e\u3002
\nArnold\u5199\u4ee5\u4e0a\u8fd9\u4e9b\u8bdd\u7684\u7528\u610f\u662f\u8bf4\uff1a\u4e18\u7b49\u4eba\u7684\u5de5\u4f5c\u6ca1\u6709\u65b0\u601d\u60f3\uff0c\u4e0d\u8fc7\u662f\u5728\u201c\u9489\u9a6c\u638c\u201d\u3002\u5f53\u7136
\n\u4ed6\u4e0d\u4fbf\u76f4\u8bf4\uff0c\u6240\u4ee5\u515c\u4e86\u4e00\u4e2a\u5927\u5708\u5b50\u3002<\/p>\n
\u79c1\u4e0b\u91cc\uff0cArnold\u5411\u8bb8\u591a\u4eba\u6beb\u4e0d\u9690\u6666\u5730\u8bf4\u4e18\u5077\u7a83\u4e86Givental\u7684\u601d\u60f3\uff0c\u4e18\u66fe\u591a\u6b21\u6253\u7535\u8bdd\u95ee
\nGivental\u5404\u79cd\u95ee\u9898\uff0cGivental\u8be6\u7ec6\u5730\u89e3\u7b54\u4e86\u4ed6\u7684\u6240\u6709\u95ee\u9898\u3002Arnold\u8fd8\u63ed\u53d1\uff0c\u4e18\u66fe\u7ecf\u4f01\u56fe\u540c
\n\u4ed6\u8fdb\u884c\u4ea4\u6613\uff1a\u7531Yau\u51fa\u9762\u5e2eGivental\u5728\u7f8e\u56fd\u627e\u5de5\u4f5c\uff0c\u800cArnold\u5e2eYau\u7684\u5f1f\u5f1f\u8bbe\u6cd5\u83b7\u5f97\u5728ICM
\n\u4e0a\u4f5c\u62a5\u544a\u7684\u9080\u8bf7\u3002\u8fd9\u5f53\u7136\u88abArnold\u62d2\u7edd\u4e86\u3002<\/p>\n
\u4e0d\u4e45\u524d\uff0c\u4e18\u8981\u4ed6\u7684\u4e00\u4e2a\u5b66\u751f\u8f6c\u544a\u56fd\u5185\u67d0\u9662\u58eb\uff1a\u4e18\u8981\u6c42\u6210\u4e3a\u8be5\u9662\u58eb\u4e0e\u4e00\u4f4d\u4e2d\u56fd\u5b66\u8005\uff08\u76ee\u524d\u5728
\n\u7f8e\u4efb\u6559\uff09\u5408\u5199\u7684\u4e00\u672c\u4e66\u7684\u5171\u540c\u4f5c\u8005\u3002\u4e18\u672c\u4eba\u4e00\u4e2a\u5b57\u4e5f\u6ca1\u6709\u5199\uff0c\u53ea\u662f\u770b\u5230\u4e86\u8be5\u4e66\u7684\u9884\u5370\u672c\u3002
\n\u4e18\u7684\u4f01\u56fe\u6700\u7ec8\u6ca1\u6709\u5f97\u901e\uff0c\u4f46\u542c\u5230\u8fd9\u4ef6\u4e8b\u7684\u4eba\u90fd\u641e\u4e0d\u61c2\uff0c\u4e18\u5df2\u7ecf\u662f\u5982\u6b64\u6709\u540d\u7684\u5b66\u8005\uff0c\u4e3a\u4f55\u8fd8
\n\u8352\u5510\u5230\u8981\u62a2\u593a\u522b\u4eba\u7684\u8457\u4f5c\uff1f <\/p>\n
5\uff0e\u53ef\u7b11\u7684\u81ea\u6211\u5439\u5618\u3002<\/p>\n
\u4eca\u5e74\u590f\u5929\u5728\u5c71\u4e1c\u5a01\u6d77\u53ec\u5f00\u4e86\u201c\u4e2d\u56fd\u6570\u5b66\u4f1a70\u5468\u5e74\u5e74\u4f1a\u201d\uff0c\u8bf7\u6765\u4e86\u56fd\u9645\u4e0a\u6700\u8457\u540d\u7684\u4e00\u4e9b\u6570\u5b66
\n\u5bb6\uff0c\u5982John Ball\uff08IMU\u73b0\u4efb\u4e3b\u5e2d\uff09\uff0cNoga Alon\uff08ICM2006\u7a0b\u5e8f\u59d4\u5458\u4f1a\u4e3b\u5e2d\uff09\uff0cMartin
\nGroetschel\uff08IMU\u6267\u59d4\uff09\uff0cJ. P. Bourguignon\uff08IHES\u4e3b\u4efb\uff09\uff0cE. I. Zelmanov\uff08\u83f2\u5c14\u5179\u5956
\n\u5f97\u4e3b\uff09\u3002\u4e18\u6210\u6850\u5728\u4f1a\u4e0a\u4f5c\u4e86\u9898\u4e3a\u201c\u51e0\u4f55\u5206\u6790\u201d\u7684\u62a5\u544a\uff0c\u7528\u4e2d\u6587\u8bb2\uff0c\u540c\u65f6\u653e\u82f1\u6587\u5e7b\u706f\u7247\u3002\u62a5
\n\u544a\u4f1a\u540e\u4e00\u4f4d\u8457\u540d\u6570\u5b66\u5bb6\u5bf9\u4eba\u8bb2\uff1a\u201cThere are too many Yau\u2019s and I\u2019s full of
\nslides\uff0creally mad.\u201d \u8fd9\u786e\u5b9e\u662f\u4e18\u70ed\u8877\u4e8e\u5439\u5618\u7684\u4e00\u4e2a\u5199\u7167\u3002<\/p>\n
\u53bb\u5e7412\u6708\uff0c\u6570\u5b66\u5927\u5e08\u9648\u7701\u8eab\u6559\u6388\u4e0d\u5e78\u4e0e\u4e16\u957f\u8f9e\u3002\u9648\u5148\u751f\u7684\u5c38\u9aa8\u672a\u5bd2\uff0c\u4e18\u6210\u6850\u5c31\u8feb\u4e0d\u53ca\u5f85\u5730
\n\u901a\u8fc7\u5a92\u4f53\u5ba3\u5e03\uff1a\u201c\u4e2d\u534e\u6570\u5b66\u5df2\u8fdb\u5165\u4e18\u6210\u6850\u65f6\u4ee3\u201d\uff08\u89c1\u300a\u5149\u660e\u65e5\u62a5\u300b2005.1.11\u8bb0\u8005\u6587\u7ae0\uff09\u3002\u4ee5\u6b64\u4e3a\u9898\u76ee\u7684\u62a5\u9053\u6587\u7ae0\u5145\u6ee1\u4e86\u5bf9\u4e18\u7684\u5439\u6367\uff0c\u6bd4\u5982\u201c\u534e\u4eba\u6570\u5b66\u5bb6\u7684\u9886\u8896\u201d\uff0c\u201c\u8fd1\u56db\u5206\u4e4b\u4e00\u4e16\u7eaa\u91cc\u6700\u6709\u5f71\u54cd\u7684\u6570\u5b66\u5bb6\u201d\u7b49\u3002\u5c24\u5176\u53ef\u7b11\u7684\u662f\uff0c\u628aI. M. Singer\u7684\u4e00\u53e5\u73a9\u7b11\u8bdd\u4e5f\u62ff\u6765\u5439\uff0c\u8bf4\u4ec0\u4e48\u201c\u5373\u4f7f\u5728\u54c8\u4f5b, \u4e18\u6210\u6850\u4e00\u4e2a\u4eba\u5c31\u662f\u4e00\u4e2a\u6570\u5b66\u7cfb\u201d\u3002\u76f8\u4fe1Singer\u8981\u662f\u77e5\u9053\u6b64\u4e8b\uff0c\u4e00\u5b9a\u4f1a\u7b11\u7834\u809a\u76ae\u3002<\/p>\n
\u5728\u4e18\u6210\u6850\u5199\u7684\u6587\u7ae0\u201c\u6570\u5b66\u4e0e\u4e2d\u56fd\u6587\u5b66\u7684\u6bd4\u8f83\u201d\u4e2d\uff0c\u4ed6\u8bf4\uff1a\u201c\u6211\u82b1\u4e86\u4e94\u5e74\u5de5\u592b\uff0c\u7ec8\u4e8e\u627e\u5230\u4e86
\n\u5177\u6709\u8d85\u5bf9\u79f0\u7684\u5f15\u529b\u573a\u7ed3\u6784\uff0c\u5e76\u5c06\u5b83\u521b\u9020\u6210\u6570\u5b66\u4e0a\u7684\u91cd\u8981\u5de5\u5177\u3002\u5f53\u65f6\u7684\u5fc3\u5883\uff0c\u53ef\u4ee5\u7528\u4ee5\u4e0b\u4e24
\n\u53e5\u6765\u63cf\u8ff0\uff1a\u201c\u843d\u82b1\u4eba\u72ec\u7acb\uff0c\u5fae\u96e8\u71d5\u53cc\u98de\u201d\u3002\u201d\u8fd9\u4e2a\u725b\u76ae\u5439\u5f97\u672a\u514d\u5927\u4e86\u4e00\u70b9\u3002\u4ece\u4e0a\u4e0b\u6587\u4e0d\u96be
\n\u770b\u51fa\uff0c\u4e18\u5728\u8fd9\u91cc\u6240\u8bf4\u201c\u5177\u6709\u8d85\u5bf9\u79f0\u7684\u5f15\u529b\u573a\u7ed3\u6784\u201d\u5b9e\u9645\u4e0a\u5c31\u662f\u6240\u8c13\u7684\u201cCalabi-Yau\u6d41
\n\u5f62\u201d\u3002\u6309\u7167\u8457\u540d\u7406\u8bba\u7269\u7406\u5b66\u5bb6Witten\u7684\u8bf4\u6cd5\uff0c\u4e3a\u4e86\u514b\u670d\u91cf\u5b50\u5f15\u529b\u7684\u56f0\u96be\u7269\u7406\u5b66\u5bb6\u53d1\u660e\u4e86
\n\u201c\u5f26\u8bba\u201d\uff0c\u800c\u76f4\u52301984-85\u5e74\u5f26\u8bba\u624d\u53d6\u5f97\u4e86\u7b2c\u4e00\u6b21\u91cd\u8981\u7a81\u7834\uff0c\u6784\u9020\u51fa\u4e00\u79cd\u80fd\u628a\u91cf\u5b50\u529b\u5b66\u4e0e
\n\u7279\u6b8a\u76f8\u5bf9\u8bba\u653e\u5728\u4e00\u8d77\u7684\u5f26\u7406\u8bba\u3002\uff08\u89c1\u201cMathematics: Frontiers and Perspectives\u201d\u7b2c
\n347-350\u9875\uff09\u4e18\u8bc1\u660eCalabi-Yau\u6d41\u5f62\u7684\u5b58\u5728\u6027\u662f\u57281977\u5e74\uff0c\u6b63\u662fWitten\u548cStrominger\u7b49\u4eba
\n\uff081985\uff09\u7b2c\u4e00\u6b21\u628aCalabi-Yau\u6d41\u5f62\u5f15\u8fdb\u5230\u5f26\u8bba\u4e2d\uff0c\u4f5c\u4e3a\u4ed6\u4eec\u7684\u7406\u8bba\u7684\u51e0\u4f55\u7ed3\u6784\u7684\u91cd\u8981\u90e8
\n\u5206\u3002\u5728\u8fd9\u4e4b\u540e\u4e18\u624d\u5f00\u59cb\u4e86\u89e3Calabi-Yau\u6d41\u5f62\u7684\u7269\u7406\u610f\u4e49\u3002\u6240\u4ee5\u6b63\u786e\u7684\u8bf4\u6cd5\u5e94\u5f53\u662f\uff1a\u662f
\nWitten\u7b49\u4eba\u53d1\u73b0\u4e86\u201c\u5177\u6709\u8d85\u5bf9\u79f0\u7684\u5f15\u529b\u573a\u7ed3\u6784\u201d\u3002\u4e18\u6210\u6850\u4f01\u56fe\u7528\u201c\u5077\u5929\u6362\u65e5\u201d\u548c\u201c\u79fb\u82b1\u63a5
\n\u6728\u201d\uff08\u4e5f\u53ef\u4e0e\u201c\u4e2d\u56fd\u6587\u5b66\u201d\u76f8\u6bd4\u8f83\uff0c\u4e00\u7b11\uff09\u7684\u624b\u6cd5\u8d2a\u5929\u529f\u4e3a\u5df1\u6709\uff0c\u53ea\u80fd\u6b3a\u9a97\u666e\u901a\u8001\u767e\u59d3\uff0c
\n\u76ee\u7684\u662f\u795e\u5316\u81ea\u5df1\u3002 <\/p>\n
\u5173\u4e8e\u4e18\u6210\u6850\u5148\u751f\u4e0e\u5b66\u672f\u8150\u8d25\u6709\u5173\u7684\u4e8b\u60c5\u8fd8\u6709\u5f88\u591a\u3002\u6211\u7684\u4e86\u89e3\u80af\u5b9a\u4e0d\u591f\u5168\u9762\uff0c\u6b22\u8fce\u5927\u5bb6\u8865
\n\u5145\u3002\u6700\u540e\u8bf7\u8bfb\u8005\u601d\u8003\u4e00\u4e0b\uff1a\u8fd9\u6837\u7684\u4e00\u4e2a\u4eba\uff0c\u81ea\u5df1\u5c31\u662f\u5b66\u672f\u8150\u8d25\u7684\u5178\u578b\uff0c\u600e\u4e48\u4f1a\u771f\u5fc3\u53cd\u5bf9\u5b66
\n\u672f\u8150\u8d25\u5462\uff1f<\/p>\n
\u7ed3\u675f\u8bed\u3002<\/p>\n
\u6570\u5b66\u662f\u6700\u7406\u6027\u7684\u79d1\u5b66\uff0c\u5b83\u4e5f\u672c\u5e94\u662f\u79d1\u5b66\u4e2d\u6700\u6d01\u51c0\u7684\u4e00\u7247\u5723\u571f\uff0c\u8fdc\u79bb\u4e16\u4fd7\u7684\u540d\u5229\u548c\u6743\u529b\u4e4b
\n\u4e89\u3002\u800c\u6570\u5b66\u5bb6\u5219\u5e94\u6f5c\u5fc3\u5b66\u672f\uff0c\u9119\u89c6\u865a\u540d\u5b9e\u5229\uff0c\u552f\u4e00\u5411\u5f80\u7684\u662f\u81f3\u9ad8\u65e0\u4e0a\u7684\u79d1\u5b66\u5883\u754c\u3002\u7136\u800c\u773c
\n\u524d\u7684\u73b0\u5b9e\u79bb\u5f00\u8fd9\u6837\u7684\u7406\u60f3\u5b9e\u5728\u592a\u8fdc\u3002\u8bb8\u591a\u7684\u73b0\u5b9e\u751a\u81f3\u662f\u76f8\u5f53\u7684\u4e11\u6076\uff0c\u5374\u88ab\u201c\u89c1\u591a\u800c\u4e0d
\n\u602a\u201d\u3002\u7b14\u8005\u5199\u4e0b\u4ee5\u4e0a\u8fd9\u4e9b\u62ab\u9732\u4e11\u6076\u7684\u6587\u5b57\uff0c\u5b9e\u51fa\u65e0\u5948\u3002\u5982\u679c\u5750\u89c6\u5e74\u8f7b\u7684\u5b66\u751f\u548c\u6570\u5b66\u5de5\u4f5c\u8005
\n\u5728\u4e0d\u77e5\u4e0d\u89c9\u4e2d\u88ab\u6c61\u79fd\u7684\u5b66\u672f\u7a7a\u6c14\u6240\u8150\u8680\uff0c\u6211\u4eec\u6570\u5b66\u5bb6\u7684\u9053\u5fb7\u826f\u5fc3\u4f55\u5728\uff1f\u4e2d\u56fd\u6570\u5b66\u7684\u524d\u9014\u53c8
\n\u5c06\u4f55\u5728\uff01 <\/p>\n
2005\uff0e10\uff0e4-6<\/p>\n
http:\/\/www1.bbsland.com\/education\/messages\/240414.html
\nhttp:\/\/www1.bbsland.com\/education\/messages\/240579.html
\nhttp:\/\/www1.bbsland.com\/education\/messages\/240760.html<\/p>\n","protected":false},"excerpt":{"rendered":"
\u9001\u4ea4\u8005: \u5929\u5730\u6b63\u6c14 2005\u5e7410\u670804\u65e507:29:22 \u4e8e [\u6559\u80b2\u4e0e\u5b66\u672f]http:\/\/www.bbsland.com \u4eca\u5e74\u4ee5\u6765\u4e18\u6210\u6850\u5148\u751f\u5728\u5404\u79cd\u5a92\u4f53\u4e0a\u53d1\u8868\u4e86\u4e00\u7cfb\u5217\u53cd\u5bf9\u201c\u5b66\u672f\u8150\u8d25\u201d\u7684\u8a00\u8bba\uff0c \u4fe8\u7136\u4ee5\u53cd\u8150\u82f1\u96c4\u7684\u59ff\u6001\u62a8\u51fb\u56fd\u5185\u6559\u80b2\u548c\u79d1\u6280\u754c\u7684\u201c\u5b66\u672f\u8150\u8d25\u201d\u3002\u672c\u4eba\u4ee5\u4e3a\uff1a \u6253\u51fa\u201c\u53cd\u8150\u8d25\u201d\u7684\u65d7\u53f7\u56fa\u7136\u53ef\u4ee5\u5f15\u6765\u8bb8\u591a\u8d5e\u540c\u548c\u652f\u6301\uff0c\u7136\u800c\u5176\u8a00\u8bba\u4e2d\u5145\u6ee1\u4e86 \u592a\u591a\u5bf9\u4e8b\u5b9e\u7684\u6b6a\u66f2\u548c\u6b66\u65ad\uff0c\u7279\u522b\u662f\u628a\u706b\u529b\u8fc7\u4e8e\u96c6\u4e2d\u4e8e\u5317\u5927\u548c\u4ed6\u4ee5\u524d\u7684\u5b66\u751f 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