2008年07月21日（开会日期：2008年7月21~30日）

2008年华东师范大学数学系
几何分析暑期学校及讨论班

时间: 2008年7月21-30.

地点: 华东师大数学系

委员会组织成员:

周培能(Bennett Chow), benchow@math.ucsd.edu

沈纯理(主席), cshen@math.ecnu.edu.cn

周风(系主任), fzhou@math.ecnu.edu.cn

郑宇, zhyu@math.ecnu.edu.cn



内容简介：

2008年7月21-30日，在华东师大数学系将举办为期近2周的几何分析暑期学校及几何分析研讨班。其中对于几何分析暑期学校, 将届时邀请国外在黎曼几何及几何分析领域十分活跃的数学家分别进行3个系列90分钟的学术讲座，同时将在7月27-30日邀请国内外部分此领域研究中的学者, 举办为期4天的几何分析研讨会，包括1小时的学术报告及学术研讨与交流活动。本次暑期学校将邀请如下3位演讲者：

1． Kaehler geometry：

演讲者：

1. Ben Weinkove, Harvard University, Mathematics Department

2. Duong Phong, Columbia University，MathematicsDepartment

2. Mean Curvature Flow

演讲者： Klaus Ecker,

Department of Mathematics and Information, Freie University, Berlin

本次暑期活动的主要目的就是面向周边学校的研究生与青年教师，通过系列讲座及学术会议的交流，介绍某些当今黎曼几何及几何分析领域上最新进展及相关研究的基本技术与理论， 进而通过与在此方面在国际上十分活跃的数学家的交流，实现提高青年教师与研究生在黎曼几何及几何分析领域上的研究水平。

2008年07月05日（开会日期：2008年7月5日-23日）

关于组织参加“2008上海市研究生暑期学校（图论与算法）”的通知
为进一步激发研究生的创新热情，提高研究生的培养质量，充分利用国内外优质教学资源，促进上海市各高校研究生全方位、多视角的交流，达到开阔视野、启迪智慧、提高创新能力的目的，在上海市学位委员会的大力支持下，由华东师范大学数学系承办2008上海市研究生“图论与算法”暑期学校。2008上海市研究生暑期学校（图论与算法）是上海市研究生教育创新项目，以“加强基础、促进交流、开拓视野、培养青年科研后备人才、提高研究生综合素质”为宗旨，聘请国内外学术水平高、教育经验丰富的知名专家、学者担任主讲教师。讲授若干基础课程，介绍学科领域的学术发展动态和最新研究成果。培养青年教师及研究生的创新意识，促进校际交流与合作，提高青年科研工作者的综合素质。本次暑期学校，自2008年7月5日开始至7月23日结束，7月4日报到，7月5日开幕，7月23日下午结束。学员结束时进行考核，考核合格者颁发相应证书，学员所在单位据此认可学分（一般2-4个学分）。

讲授专家

主讲教师为国内外学术水平高、教学经验丰富的知名专家、学者担任，包括美国明尼苏达大学堵丁柱教授(Advances in Analysis and Design of Approximation Algorithms)、美国西佛吉尼亚大学张存铨教授(Integer Flows and Cycle Covers of Graphs)，还有其他有关专家（包括范更华、雷吉仕、邵嘉裕、高志诚、周青、殷剑兴、康丽英、李雨生、吕长虹、任? 韩、束金龙、张晓东，赖虹建等）作讲座。

招生对象及规模

本次暑期学校主要面向上海市高校及研究单位中具有一定图论及组合数学基础的硕士生、博士生、青年教师，同时也邀请全国其他高校及研究机构的学者和年轻学生参加。招收正式学员100名。学员由所在单位推荐、上海市研究生暑期学校（图论与算法）学术委员会资格审核及录取。

学员待遇安排

本次暑期学校将为正式学员提供免费住宿及教材、讲义等学习资料，并每天提供十元的伙食补贴。

报名时间和方式

本次暑期学校报名截止时间为2008年5月20日。正式录取名单将于2008年6月10日在网站公布，并发出正式录取通知书。
请将报名表通过电子邮件发送到 workshop@math.ecnu.edu.cn ,附件请用您的学校或单位加名字命名。
欢迎广大研究生报名参加“2008上海市研究生暑期学校(图论与算法)”！我们将于2008年4月底公布2008上海市研究生暑期学校(图论与算法)专用网页网址。

附: 2008上海市研究生暑期学校(图论与算法)报名表

华东师范大学数学系
2008.4.8

2008年07月05日（开会日期：2008-07-11~31）

2008年暑期学校 偏微分方程讲习班课程

Place: The Science Building A1510
Date: July 11- July 31
Time: tentative
1． Exploring the Roles of Diffusion Rates in Reaction-Diffusion Systems
Speaker: Prof. Wei-Ming NI(University of Minnesota,USA and ECNU)
1. Activator-Inhibitor Systems: An Overview
2. Global Existence of Shadow Systems
3. Finite-time Bolw-up of Shadow Systems
4. Stability Properties of Shadow Systems
5. CIMA Reaction and Related Topics
ABSTRACT: We will discuss how the dynamics of solutions to reaction-diffusion systems depend on the diffusion rates. Particular examples, including Gierer-Meinhardt activator-inhibitor system and the Lengyel-Epstein system for the CIMA reaction, will be used to illustrate this point of view, and special attention will be given to the corresponding shadow systems. Comparisons will be made among the 2x2 reaction-diffusion systems, their shadow systems, and the kinetic systems.

2. Allen-Cahn Type Equations in Phase Transition
Speaker: Prof. Gui ChangFeng (University of Connecticut, USA)

3. Maximum principle, symmetry and some classical elliptic equations
Speaker: Prof. Ye Dong (Univesité de Cergy-Pontoise, France)

2008年07月02日（开会日期：2008年7月10日-24日）

Summer School on Quantum Groups and Lie Theory in ECNU 2008
2008华东师大数学系研究生暑期学校(Time Table)
《量子群和李理论海外专家系列讲学活动》
（2008年7月10日---7月24日）
Organizer: Prof. Dr. Naihong HU
Lecture (I) ---Nichols Algebras of Diagonal Type
by I. Heckenberger (德国慕尼黑)
Abstract: The theory of Nichols algebras of diagonal type has its origins in a work of W. Nichols from 1978 as he tried to classify a class of finite dimensional Hopf algebras. Since the discovery of quantum groups by Drinfel’d and Jimbo it is known that Nichols algebras are closely related to the theory of semisimple Lie algebras and Lie superalgebras. Later it turned out that all Nichols algebras of diagonal type hold a combinatorics which is a nontrivial generalization of the combinatorics of Weyl groups and associated root systems, and these structures admit a full classification of (say finite dimensional) Nichols algebras of diagonal type. The knowledge of the structure of Nichols algebras of diagonal type is crucial for the method of Andruskiewitsch and Schneider to classify all pointed Hopf algebras with finite Gelfand-Kirillov dimension and abelian coradical. In this course an introduction to Nichols algebras (of diagonal type) and their combinatorics is given, and some examples are presented. The classification scheme is sketched, and further related constructions like Drinfel’d doubles, Lusztig isomorphisms are explained.
课程目录：（每讲2小时）
1. Hopf algebras and braided Hopf algebras
2. Nichols algebras
3. Kharchenko's PBW basis of Nichols algebras of diagonal type
4. Weyl groupoids
5. Root systems of Nichols algebras of diagonal type
6. Classification of finite Nichols algebras of diagonal type
7. Drinfeld doubles of Nichols algebras of diagonal type and Lusztig isomorphisms
8. Outlook

Lecture (II)--- The Tensor Product Theory for Modules for Affine Lie Algebras of Fixed Levels
By Huang Yi-Zhi (美国Rutgers)
Abstract: For a suitable category of modules for an affine Lie algebra of a negative level, Kazhdan and Lusztig first constructed a rigid braided tensor category structure on the category. In the context of the representation theory of vertex operator algebras, Lepowsky and I constructed, among many other things,
a braided tensor category structure on the category of finite direct sums of integrable highest weight modules for an affine Lie algebra of a positive integral level. Using the verlinde conjecture I proved, I proved the rigidity and the non-degeneracy property of the braided tensor category. Recently Lepowsky, Zhang and I developed a logarithmic tensor product theory which includes the theory of Kazhdan-Lusztig and the early theory of Lepowsky and I mentioned above as special cases. In these lectures, I will explain this general tensor product theory in the special case of affine Lie algebras.

课程目录：（每讲2小时）
1. Affine Lie algebras and modules
2. Vertex operator algebras associated to affine Lie algebras,modules and (logarithmic) intertwining operators
3. Definitions of braided tensor category and modular tensor category
4. Tensor product bifunctor and its constructions
5. Differential equations of regular singularities
6. Associativity and commutativity isomorphisms
7. The coherence properties, rigidity and nondegeneracy property
Lecture (III)--- Introduction to Extended Affine Lie Algebras
By Gao Yun (加拿大约克)
Abstract: Extended affine Lie algebras are a natural generalization of affine Kac-Moody Lie algebras. They are closely related to the extended affine root systems of K.Saito, interesction matrix Lie algebras of P.Slodowy, and root graded Lie algebras studied by Berman-Moody, Benkart-Zelmanov, Neher, Allison-Benkart-Gao, Benkart-Smirnov. This newly developed Lie algebras include toroidal Lie algebras as examples. In this series of lectures, I will give definitions and many examples. Then I will show how those Lie algebras can be classified by relating with the extended affine root systems and using the root graded Lie algebras. Finally I will provide some module constructions for some of extended affine Lie algebras.
课程目录：（每讲2小时）
1. Definitions of EALAs
2. Examples of EALAs
3. Classifications: Root systems
4. Classifications: Lie algebras I--Associative coordinates
5. Classifications: Lie algebras II--Alternative coordinates
6. Classifications: Lie algebras III--Jordan coordinates
7. Representation theory: Vertex operator construction
8. Representation theory: Boson and fermi construction


Lecture (IV)--- Vertex Representations of Affine Lie Algebras and Generalizations
By Jing Naihuan (美国北卡)
Abstract: Affine Lie algebras are the most important examples of Kac-Moody Lie algebras, and many of the finite-dimensional Lie theory can be generalized to the infinite dimensional case. In this course we will discuss some of the special features of affine Lie algebras and their representations. We will start with the simplest example of the affine Lie algebra sl^(2) to explain its two commonly used vertex operator realizations: the homogeneous and principal picture. We then move forward to more general affine Lie algebras and present its vertex representations (mostly level one). In the end we hope to briefly discuss some of the generalizations such as quantum groups and vertex (operator) algebras. This introductory short course consists of eight lectures, and a list of the detailed topics are as follows.
课程目录：（每讲2小时）
1) Affine Lie algebras
Kac-Moody Lie algebras, realizations of affine Lie algebras
2) Weyl groups, affine Weyl groups
3) Representations of Affine Lie algebras
Category O, and general theory of highest weight modules, Verma modules, Character formula
4) Heisenberg algebras
Uniqueness of irreducible representations, identification with differential operators on the polynomial ring.
5) Homogeneous vertex representations of affine Lie algebras
Representations of the affine Lie algebra sl^(2), generalization to ADE cases
6) Principal vertex representations of affine Lie algebras
Examples of classical affine Lie algebras sl^(n)
7) Sugawara operators and representations of the Virasoro algebra
8) Generalizations to quantum affine Lie algebras, vertex operator algebras

Lecture (V)---Hopf Algebras with Trace and Representation
By Marc Rosso (法国巴黎高师)
Abstract: We study the restriction of representations of Cayley-Hamilton algebras to subalgebras. This theory is applied to determine tesor products and branching rules for representation of quantum groups at roots of 1.







课程目录：（每讲1小时）
1）n-dimensional representations
2）Cayley-Hamilton algebras
3）Semisimple representations
4）The reduced trace
5）The unramified locus and restriction maps
6）Quantized universal enveloping algebras at roots of 1
7）Clebsch-Gordan decompositions for generic representations of quantized universal enveloping algebras at roots of 1.

Lecture (VI)---Representations and Cohomology for Lie Superalgebras
By Jonathan Kujawa (Oklahoma)

Abstract: In this series of lectures we will provide an introduction to some recent developments in the representation theory of Lie superalgebras. We will articularly emphasize recent work of ours (in collaboration with Bagci, Boe, and Nakano) on cohomology and support varieties. In particular, we will see that we are able to adapt tools from finite groups in positive characteristic to obtain new
insights into the characteristic 0 theory of Lie superalgebras. We also will discuss recent work of ours and others which shows that the combinatorics of crystals
(in the sense of Kashiwara) controls the representation theory of Lie superalgebras. The topics and depth of the talks will depend on the audience's interests and background. Every effort will be made to make the lectures accessible all attendees.
课程目录：（每讲1小时）
1) Preliminary to Lie superalgebras
2) Cohomology and support varieties
3) Crystals in super cases
4) Recent advances in representations of Lie superalgebras (I)
5) Recent advances in representations of Lie superalgebras (II)

7月23日至24日为两天的短会---《量子群与李理论会议》 （拟安排12个报告）

致谢：
本次暑期班活动受到学校国际交流处、研究生院、数学系111引智计划项目、数学系教育部“代数几何与表示论”创新团队项目以及景乃桓与胡乃红的合作项目杰青（B类）的支持。

2008年06月19日（开会日期：2008年6月17日~26日）

研究生短课程《自由边界问题》
Lectures on Free Boundary Problems
主讲人 Professor Fanghua Lin （New York University）
（5） 6月17日星期二，下午2：00-4：00
地点：中山北路校区理科大楼A-510
（6） 6月18日星期三，下午2：00-4：00
地点：中山北路校区理科大楼A-1414
（7） 6月19日星期四，下午2：00-4：00
地点：中山北路校区理科大楼A-510
（8） 6月20日星期五，下午2：00-4：00
地点：中山北路校区理科大楼A-510
（9） 6月23日星期一，下午2：00-4：00
地点：中山北路校区理科大楼A-510
（10） 6月24日星期二，下午2：00-4：00
地点：中山北路校区理科大楼A-510
（11） 6月25日星期三，下午2：00-4：00
地点：中山北路校区理科大楼A-510
（12） 6月26日星期四，下午2：00-4：00
地点：中山北路校区理科大楼A-1414