最近事多，今天只好匆匆更新一下。
我的学生高显于5月12日顺利通过博士学生论文答辩。
下学期他将去法国巴黎高师、巴黎大学和巴黎第七大学（德尼·狄德罗大学）做博士后。
最后是三张答辩时的照片。
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最近Vafa一直鼓吹他的F理论唯象学，认为在LHC上有一些比较确定的效应。特别是当D7膜上的理论与引力脱耦时，理论有一些确定的预言。关于F理论唯象学，见
GUTs and Exceptional Branes in F-theory – II: Experimental Predictions
和
F-theory and the LHC: Stau Search
Heckman和Verlinde最近发现，要求D7膜脱耦等价于D7膜绕在非对易的four cycle上，four cycle上有有限个fuzzy点，点的个数与大统一耦合强度有关，非常有意思。
摘要：
We show that in the decoupling limit of an F-theory compactification, the internal directions of the seven-branes must wrap a non-commutative four-cycle S. We introduce a general method for obtaining fuzzy geometric spaces via toric geometry, and develop tools for engineering four-dimensional GUT models from this non-commutative setup. We obtain the chiral matter content and Yukawa couplings, and show that the theory has a finite Kaluza-Klein spectrum. The value of 1/alpha_(GUT) is predicted to be equal to the number of fuzzy points on the internal four-cycle S. This relation puts a non-trivial restriction on the space of gauge theories that can arise as a limit of F-theory. By viewing the seven-brane as tiled by D3-branes sitting at the N fuzzy points of the geometry, we argue that this theory admits a holographic dual description in the large N limit. We also entertain the possibility of constructing string models with large fuzzy extra dimensions, but with a high scale for quantum gravity.
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