主 题: [绗?6鏈熷寳浜?ぇ瀛︾壒鍒?暟瀛﹁?搴?Fano娴佸舰涓奒ahler-Einstein搴﹂噺闂??
报告人: 鏉庨┌
时 间: 2013-06-17 08:00 - 2013-06-28 18:00
地 点: 鏁板?涓?績鍏ㄦ枊9鏁欏?
绗?6鏈熷寳浜?ぇ瀛︾壒鍒?暟瀛﹁?搴э紝鏃堕棿鏄?013.6.17-6.28锛屾瘡鍛ㄧ殑涓€銆佷笁銆佷簲鐨勪笅鍗?4:00-16:00, 鍦扮偣:鏁板?涓?績鍏ㄦ枊9鏁欏?.
鏉庨┌锛氭湰绉戝拰纭曞＋姣曚笟浜庡寳浜?ぇ瀛︽暟瀛﹀?闄?紝2007-2012鍦ㄦ櫘鏋楁柉椤垮ぇ瀛︽暟瀛︾郴甯堜粠鐢板垰鏁欐巿锛岀幇鍦ㄥ湪绾界害宸炲窞绔嬪ぇ瀛︾煶婧?垎鏍″仛鍗氬＋鍚庣爺绌躲€傜爺绌舵柟鍚戞槸澶嶅嚑浣曘€
棰樼洰锛欶ano娴佸舰涓奒ahler-Einstein搴﹂噺闂??
澶х翰锛氭渶杩慘ahler鍑犱綍涓?竴涓?噸瑕佸彂灞曟槸Yau-Tian-Donaldson鐚滄祴鐨勮В鍐炽€傝繖涓?寽娴嬫妸Fano娴佸舰鐨勮В鏋愭€ц川鍜屼唬鏁版€ц川绱у瘑鍦拌仈绯昏捣鏉ワ紝瀵笷ano娴佸舰鐨勭爺绌跺甫鏉ラ噸瑕佺殑淇℃伅銆傛垜浠?皢璁ㄨ?Kahler-Einstein搴﹂噺闂??涓?竴浜涢噸瑕佺殑姒傚康鍜屾柟娉曘€傝繖闂ㄧ畝鐭?殑璇剧▼鏄?檰蹇楀嫟鏁欐巿鐨凨ahler鍑犱綍璇剧▼鐨勫欢缁?€備互涓嬫槸瀹夋帓鐨勫唴瀹广€
1a: 寮曡?锛欿ahler-Einstein搴﹂噺闂??鍜孴ian鐨勭翰棰? 1b: Futaki 涓嶅彉閲忥細瑙ｆ瀽瀹氫箟.
2a: Futaki 涓嶅彉閲忥細浠ｆ暟瀹氫箟. 2b: K-绋冲畾鎬у拰Chow绋冲畾鎬э紝鏈夐檺缁撮€艰繎.
3a: 鑳介噺娉涘嚱锛欴ing 娉涘嚱鍜孧abuchi 娉涘嚱. 3b: Moser-Trudinger 涓嶇瓑寮?
4a:鎵€鏈塊ahler搴﹂噺缁勬垚鐨勭┖闂寸殑鍑犱綍. 4b: Berndtsson鐨勬?璋冨拰鎬ц川瀹氱悊锛欿ahler鍑犱綍涓?殑Brunn-Minkowski涓嶇瓑寮?
5a: 甯﹂敟鍨嬪?鐐圭殑Kahler-Einstein搴﹂噺锛宭og-Futaki涓嶅彉閲 5b: log-Ding娉涘嚱鍜宭og-Mabuchi娉涘嚱锛屽?璁歌?搴︾殑鎻掑€兼€ц川.
6: Yau-Tian-Donaldson 闂??鐨勮В鍐筹紙鏍规嵁Tian鐨勬枃绔?.
Peking University sixteenth special lectures in mathematics, the time : 2013.6.17-6.28, on Monday, Wednesday, Friday 14:00-16:00 , place : Mathematics center Quan Zhai 9 classroom.
Chi Li graduated from Peking University, obtaining Bachelor and Master degree. He studied at Princeton University from 2007-2012 under the supervision of Professor Gang Tian. He is now doing his postdoc research at State University of New York at Stony Brook. His main interest is Complex Geometry.
Title: Topics in Kahler-Einstein problem on Fano manifolds.
Abstract: These will be the follow-up topic lectures after Prof. Zhiqin Lu's course on Kahler geometry. We will discuss some key concepts and techniques in the problem of Kahler-Einstein metrics which lead to the recent resolution of Yau-Tian-Donaldson conjecture.
1a: Introduction/Review of Kahler-Einstein problem. 1b: Futaki invariant I: analytic definition.
2a: Futaki invariant II: Algebraic definition. 2b: K-stability and Chow stability, finite dimensional approximation.
3a: Energy functionals: Ding energy and Mabuchi energy. 3b:Moser-Trudinger inequalities.
4a: space of Kahler metrics. 4b: Berndtsson's subharmonicity theorem: Brunn-Minkowski inequality in Kahler geometry.
5a: Conical Kahler-Einstein metrics, log-Futaki invariant. 5b:log-Ding energy and log-Mabuchi energy, interpolation of cone angles.
6. Resolution of Yau-Tian-Donaldson conjecture (after Tian).
