We will first review the recent progress in SYK models and their global impacts in quantum gravity, QCD, condensed matter physics, quantum information science and deep machine learning. Then we will outline the results achieved in our recent works in [1-5]. This colloquium is pedagogical, so should be accessible to any graduate students who are interested in working on this still rapidly expanding direction and other related directions such as many body localization (MBL), eigenstate thermalization hypothesis (ETH), Neural networks/Deep Machine learning, Complexity, etc.
1. Jinwu Ye, Two indices Sachdev-Ye-Kitaev model, ArXiv：1809.0667, substantially revised version 2 to be put on ArXiv soon
2. Fadi Sun, Yu Yi-Xiang, Jinwu Ye and WuMing Liu, A new universal ratio in Random Matrix Theory and Random matrices and quantum analog of Kolmogorov-Arnold-Moser (KAM) theorem in hybrid Type-I and Type-II Sachdev-Ye-Kitaev models, ArXiv：1809.07577.
3. Fadi Sun， Yu Yi-Xiang, Jinwu Ye and WuMing Liu, Classifications of quantum chaos in colored Sachdev-Ye-Kitaev models, arXiv:1903.02213.
4. Fadi Sun and Jinwu Ye, Periodic Table of SYK and supersymmetric SYK , arXiv:1905.07694
5. Yu Yi-Xiang, Jinwu Ye and CunLin Zhang, Photon Berry phases, Instantons, Quantum chaos and quantum analog of
Kolmogorov-Arnold-Moser (KAM) theorem in the $ U(1)/Z_2 $ Dicke models, arXiv:1903.02947
叶锦武教授是美国耶鲁大学理论物理博士。他现在是首都师范大学教授和美国密西西比州立大学教授. 叶教授主要研究领域是强相互作用的电子, 玻色子, 自旋，光子等的合作现象和量子或拓扑相变理论,