2016数学天元基金《泛函分析》专题讨论班第二期

“算子代数与非交换几何”研究生暑期学校

1st Week |
11th July |
12th July |
13th July |
14th July |
15th July |

9:30-11:15 |
Nigel Higson |
Nigel Higson |
Nigel Higson |
Nigel Higson |
Nigel Higson |

Lunch Break |
|||||

14:00-15:00 |
N. C. Phillips |
George Elliott |
N. C. Phillips |
George Elliott |
N. C Phillips |

15:20-16:20 |
Yijun Yao |
Yijun Yao |
Yijun Yao |
Yijun Yao |
Yijun Yao |

2nd Week |
18th July |
19th July |
20th July |
21st July |
22nd July |

9:30-11:15 |
Shengzhi Xu |
Shengzhi Xu |
Shengzhi Xu |
Shengzhi Xu |
Shengzhi Xu |

Lunch Break |
|||||

14:00-15:00 |
N. C. Phillips |
N. C. Phillips |
N. C. Phillips |
Huaxin Lin |
Huaxin Lin |

15:20-16:20 |
Zhuang Niu |
Zhuang Niu |
Zhuang Niu |
TBA |
TBA |

3rd Week |
25th July |
26th July |
27th July |
28th July |
29th July |

9:00-10:00 |
Ryszard Nest |
Ryszard Nest |
Ryszard Nest |
Ryszard Nest |
Ryszard Nest |

10:20-11:20 |
Quanhua Xu |
Quanhua Xu |
Quanhua Xu |
Quanhua Xu |
Quanhua Xu |

Lunch Break |
|||||

14:00-15:00 |
Guihua Gong |
Guihua Gong |
Guoliang Yu |
Guoliang Yu |
Guoliang Yu |

15:20-16:20 |
Qin Wang |
Qin Wang |
Yang Liu |
TBA |
TBA |

**课程信息**

Lecturer | Photo | Lecture Title | Lecture Plan |

The Agony and the Ecstasy---the Classification of Simple Amenable C*-algebras | I will review the history of the classification of simple amenable C*-algebras and introduce the recent classification results by Gong, Lin, Niu and me. I will also mention some future directions of the classification program. | ||

Introduction to Classification of real rank zero C*-algebras. | I will talk about some works on the classification of real rank zero C*-algebras. Such C*-algebras are natural objects in this area and enjoy rich projections in the structure. Concrete classes of reak rank zero C*-algebras appeared as inductive limit ones (etc.) will be discussed. | ||

K-Theory for Banach Algebras | Nigel Higson Lecture Information |
||

The Bott Maps and Almost Commuting Unitaries | We will introduce some useful tools in the study of the structure of C*-algebras. These include the Basic Homotopy Lemma and rotation maps. We will begin with a pair of almost commuting unitaries and the Bott map. | ||

Modular Curvature for Toric Noncommutative Manifolds | A general question behind the talk is to explore a good notion for intrinsic curvature in the framework of noncommutative geometry started by Alain Connes in the 80's. It has only recently begun (2014) to be comprehended via the intensive study of modular geometry on the noncommutative two tori. In this talk, we extend recent results on the modular geometry on noncommutative two tori to a larger class of noncommutative manifolds: toric noncommutative manifolds. (Slides) | ||

Homological Methods in Operator Algebras |
l. Triangulated structure of KK-category and related homological functors |
||

Classification of C*-algebras: AF-algebras and a little beyond | The classification of approximately finite dimensional C*-algebras (AF-algebras) will be reviewed. In particular, we shall check the roles of existence theorem and uniqueness theorem in the intertwining argument. Then, let us move slightly further and introduce the C*-algebras which can be tracially approximated by finite dimensional C*-algebras. | ||

Crossed Products by Finite Groups | N. Christopher Phillips Lecture Information |
||

Groupoids in Higher Index Problems | |||

Hypercontractivity | |||

Groupoid Algebras | |||

The Interaction of Algebraic Topological and Operator K-theory | For a Banach algebra (C*-algebra) we can define several kinds of K-theory from the point of view of topology, algebra, and analysis. I will compare the various K-theory, and give the interaction between them. | ||

Primary and Secondary Invariants of Elliptic Operators and Applications | In these lectures, I will introduce primary and secondary index invariants of elliptic operators and discuss their applications to geometry and topology. This is joint work with Shmuel Weinberger and Zhizhang Xie. |

**Group Photo**