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

Schedule & Abstracts

日程表

地点：中国，上海，华东师范大学，中山北路校区，理科大楼A楼，A1414

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
George Elliott		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.
Guihua Gong		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.
Nigel Higson		K-Theory for Banach Algebras	Nigel Higson Lecture Information (PDF)
Huaxin Lin		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.
Yang Liu		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)
Ryszard Nest		Homological Methods in Operator Algebras	l. Triangulated structure of KK-category and related homological functors 2. UCT theorem (problem) for non-simple C-algebras 3. Universal properties of the assembly map for group actions 4. Assembly map and Baum-Connes conjecture for quantum groups 5. Around C-algebras, cyclic homology, algebraic K-theory and higher categories.
Zhuang Niu		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.
N. Christopher Phillips		Crossed Products by Finite Groups	N. Christopher Phillips Lecture Information （The slides for those lectures）
Qin Wang		Groupoids in Higher Index Problems	Lecture Information
Quanhua Xu		Hypercontractivity	Lecture Information
Shengzhi Xu		Groupoid Algebras	Lecture Information
Yijun Yao		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.
Guoliang Yu		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