结构化的预处理和迭代方法与应用研讨会(SPIMA 2014)

2014-05-12 ~ 2014-05-16 512

Synopsis and Organizers

Discrete Complex Dynamics: The theory has developed fast in the last 20 years with the advent of computers. The theory consists of the Fatou theory of orderly behaviour and the Julia theory of chaotic behaviour. There has been many advances but many basic problems remain unsolved. Of these we can mention whether two competing notions of Julia sets for Henon maps are equivalent. In the Fatou theory, there are questions about classification of Fatou sets.

Continuous Dynamics: This arises in the study of polynomial vector fields. The integral curves are Riemann surfaces which foliate space. The foliation has singular points. There has been much work on understanding the global behaviour of the leaves, such as showing that under some hypotheses, leaves are dense. The use of positive harmonic currents introduced by Fornæss and Sibony has been very fruitful. A main question left is that of existence of minimal exceptional sets, arising from taking the closure of a leaf which does not cluster at any singular point. Hyperbolicity: This classical notion introduced by Kobayashi is a very active area of research. Important advances have been made in the last period, among them Siu’ work on hyperbolicity of a generic algebraic hypersurface of large degree in Cn or CPn . The methods of Demailly also play major role. The Green-Griffiths conjecture concerning almost-hyperbolicity of compact complex manifolds of general type is still a major challenge.

Holomorphic flexibility and modern Oka theory: Opposite to hyperbolicity, flexibility properties of a complex manifold signify that it admits many holomorphic maps from Euclidean spaces and other Stein manifolds. The central notion is that of an Oka manifold (Forstneriˇc 2009) which evolved from the classical Oka-Grauert principle. Among the main sufficient condition are Gromov’s ellipticity and flexibility of Arzhantsev et al. This field offers challenging problems and applications. Recent progress includes a study of directed immersion of Riemann surfaces, with emphasis on null curves and their applications to the classical Calabi-Yau problem on minimal surface.

Invariant theory in Complex Analysis: This arises when one tries to understand when are two objects holomorphically equivalent. A basic approach is to attach holomorphic invariants to the objects such as hypersurfaces. The geometric invariants are constructed using the Cartan theory, while the algebraic invariants are accessible through the Poincare-Moser normal form theory. The subject has been intensively studied in the past many years and has applications to many other problems in complex analysis.

Complex Plateau Problem and singularity theory: Singularity theory plays a very important role in algebraic geometry, differential geometry, topology, dynamic system, etc. This field offers many challenging problems among which the complex Plateau problem is one of the important ones. This problem forms an intrinsic link between CR geometry and singularity theory. The invariants theory of singularities, developed by S. Yau, has been proven very fruitful. A main open question is the interior regularity for non-hypersurface type strongly pseudoconvex CR manifolds; this is also related to the famous Hartshorne conjecture in algebraic geometry.

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Registering for Submit Abstract (not later than April 25), please visit: http://msc.tsinghua.edu.cn/scacd2014/

Organizers

Name University
Organizer
Shiu Yuen Cheng Tsinghua University, China
John Eric Fornæss Norwegian University of Science and Technology
Franc Forstneric University of Ljubljana, Slovenia
Xiaojun Huang Rutgers University, USA
Stephen S.T. Yau Tsinghua University, China
Xiangyu Zhou Chinese Academy of Sciences, Beijing

participants

Marco Abate University of Pisa, Italy
David Eugene Barrett University of Michigan, USA
Eric Douglas Bedford University of Indiana, USA
Francois Berteloot University of Toulouse, France
Florian Bertrand University of Vienna, Austria
Gautam Bharali Indian Institute of Science
Zbigniew Blocki University of Cracow, Poland
Filippo Bracci University of Rome II, Italy
Shiu-Yuen Cheng Tsinghua University
Dan Florin Coman Syracuse University, USA
Fusheng Deng University of Oslo
Pascal Dingoyan University of Paris VI, France
Barbara Drinovec Drnovšek University of Ljubljana, Slovenia
Rong Du East China Normal University   
John Erik Fornaess University of Michigan, USA
Franc Forstneric University of Ljubljana, Ljubljana, Slovenia
Siqi Fu Rutgers University-Camden, USA
Hervé Christian Gaussier Joseph Fourier University
Dusty E. Grundmeier University of Michigan, USA
Tobias Alexander Harz University of Wuppertal, Germany
Gustavo Hoepfner Universidade Federal de Sao Carlos
Jorge Guillermo Hounie  Universidade Federal de São Carlos
Zhangjian Hu Huzhou Normal College
Xiaojun Huang Rutgers University, New Brunswick, USA
Howard Joel Jacobowitz Rutgers University-Camden, USA
Mattias Orjan Jonsson University of Michigan, USA
Daniel Matthew Burns Jr University of Michigan, USA
Slawomir Kolodziej Jagiellonian University
Nikolay Kruzhilin Russian Academy of Sciences
Werner Frank Kutzschebauch University of of Berne, Switzerland
Finnur Larusson University of Adelaide, Australia
Mark Gordon Lawrence Nazarbayev University, Kazakhstan
Jiri Lebl Oklahoma State University
Matthias Stefan Leuenberger University of Berne, Switzerland
Songying Li University of California, Irvine
Taishun Liu Huzhou Normal College
Mingsheng Liu South China Normal University
Keping Lu Henan University, Kaifeng
Daowei Ma Wichita State University, USA
Benedikt Magnusson University of Iceland in Reykyavik, Iceland
Jeffery Dean McNeal Ohio State University, USA
Yanyan Niu Capital Normal University
Chunhui Qiu Xiamen University
Jasmin Raissy University of Toulouse, France
Tyson Ritter University of Oslo, Norway
Feng Rong Shanghai Jiao Tong University      
Min Ru University of Houston, USA
Mei-Chi Shaw University of Notre Dame, USA
Nikolay Shcherbina University of Wuppertal, Germany
Nessim Sibony University Paris-Sud, Orsay
Marko Slapar University of Ljubljana, Slovenia
Zhenhan Tu Wuhan University
Wei Wang Zhejiang University
Erlend Fornaess Wold University of Oslo, Norway
Jian Xiao Fudan University
Qiming Yan Tongji University
Stephen S.T. Yau Tsinghua University
Fei Ye University of Hong Kong
Sai-Kee Yeung Purdue University, USA
Wanke Yin Wuhan University
Yuan Zhang Indiana-Purdue University, USA
Mingyi Zhang Tsinghua University
Liyou Zhang Capital Normal University
Chunping Zhong Xiamen University
Xiangyu Zhou Chinese Academy of Sciences
Huaiqing Zuo Tsinghua University