Abstract：

　　We  will first review the recent  progress in SYK models and their global impacts in quantum gravity, QCD, condensed matter physics and quantum information science.   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  research direction and other related directions such as many body localization (MBL), eigenstate thermalization hypothesis (ETH)， Complexity, Machine learning, 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

Biosketch：

　　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，他的研究还涉及超对称性破缺，共形场论和各种量子或拓扑相的量子引力对偶。

　　His two most recent research directions are on

(1) Novel Quantum, topological Phases, phase transitions driven by interactions in various spin-orbit coupled systems.

(2) quantum chaos and quantum information scramblings in cavity QED systems or in Sachdev-Ye-Kitaev models.