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1 University of Science and Technology of China School of Mathematical Sciences, Hefei, Anhui, P.R.China Spring Workshop on Geometric Analysis 2011 年春季几何分析研讨会 Conference Manual 会议手册 2011 年 22-2 安徽合肥中国科学技术大学数学科学学院 1

2 报到会议安排中国科学技术大学数学科学学院时间报告题目报告人备注 Ricci flow on surfaces with 殷浩 ( 上海交大 ) conical singularities The KdV curve and 宋翀 ( 科学院 ) Schrodinger-Airy curve 茶歇报告在 On the Convergence Behavior of 陈立 ( 科学院 ) 1611 Harmonic Map Sequence from 茶歇在 Cylinders 午餐午餐在 Small Deborah number limits of 江宁 ( 科学院 ) 东区教 micro-macro polymeric flows 工餐厅 Combinatorial Ricci Flows on 葛化彬 ( 北京大学 ) Surfaces 茶歇丁伟岳院士报告前往巢湖半汤巢湖一游, 下午约返回合肥组织委员会信息会议组织委员会 : 陈秀雄郜云李嘉禹王友德秘书 : 黄力研 lynn77@ustc.edu.cn 联系电话 : 地址 : 合肥市金寨路 96 号中国科学技术大学东区数学科学学院 1613 室 2

3 报告摘要报告人 : 殷浩报告题目 :Ricci flow on surfaces with conical singularities 摘要 :In this talk, we will discuss the normalized Ricci flow on surfaces with conical singularities. We will show that under some additional assumptions, the ricci flow converges to a constant curvature metric. 报告人 : 宋翀报告题目 :The KdV curve and Schrodinger-Airy curve 摘要 :In this talk, I will introduce the notion of KdV curves and Schrodinger-Airy curves. These curves are stable solutions to the geometric KdV-Airy flow equation and Schrodinger-Airy flow equation respectively, which are proposed by Sun and Wang recently. We demonstrate that the KdV curves can be regarded as a 3-rd order analogue of geodesics. Other interesting properties and explicit examples of these curves will be addressed. In addition, we will consider a perturbed KdV curve system and show the existence of multiple solutions to this system on torus. 报告人 : 陈立报告题目 :On the Convergence Behavior of Harmonic Map Sequence from Cylinders 摘要 :In this paper, we are concerned with the convergence behavior of a sequence of harmonic maps from long cylinders with uniformly bounded energy. If the bubbling phenomenon does not occur, we give the length formula of the limit map (i.e. geodesic in the target manifold). 报告人 : 江宁报告题目 :Small Deborah number limits of micro-macro polymeric flows 摘要 :In this talk, I will the recent progress of the mathematical theory of the micro-macro polymeric flow, such as FENE ( Finitely Extensible Nonlinear Elastic) model and Oldroyd-B model. They are coupled by macroscopic fluids and microscopic polymers to describe complex fluids. The Deborah numbers measures how the complex fluid behaves like the regular fluid. When the Deborah number is small, we derive an inhomogeneous incompressible Navier-Stokes equations, i.e. the density is non-constant and the viscosity depends on the density. We justified this small Deborah number limits. This is a joint work with Fang-hua, Lin. 报告人 : 葛化彬报告题目 :Combinatorial Ricci Flows on Surfaces 摘要 :In this talk, I will say something about discrete surface Ricci flow introduced by Bennett Chow and Feng Luo. For a triangulated surface, by assigning a positive number to each vertex,which is called circle packing metric, we get a combinatorial Gaussian curvature.then discrete Ricci flow is introduced naturally as a stright forward analogy with che classical Hamilton-Ricci flow. The existence and convergence results about discrete flow will be stated, and then, several interesting questions will be posed. 3

4 参会人员名单姓名江宁陈立宋翀赵亮杨云雁韩小利祝晓宝李伟鲍超季丹丹陆宇澄殷浩赵立丰李皓昭许金兴葛化彬食宿安排住宿 : 学生 2 人一标间, 老师一人一间 ; 合肥天庭商务酒店 ( 科大店 ); 巢湖半汤远州豪庭大酒店正餐 : 自助餐, 持餐券在科大东区活动学生活动中心三楼教工食堂就餐交通及旅游信息一学校地址 : 合肥市金寨路 96 号中国科学技术大学东区管理科研楼 16 楼, 火车站乘 1 路 226 路公交车到中国科技大学站下, 打车约 15 元二合肥天庭商务酒店 ( 科大店 ), 合肥市金寨路 161 号黄山路与金寨路交叉口, 电话 : 步行至科大数学学院约 5 分钟旅游巴士 : 23 下午 17:30 在数学院楼下发车前往巢湖半汤

5 附 : 科大校区地图天庭商务酒店在这里数学科学学院楼 : 东区管理科研楼楼科大校园东校区餐券用餐地点 : 教工食堂东区活动中心三楼 5

Introduction to Hamilton-Jacobi Equations and Periodic Homogenization

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