華東師范大學(xué)數(shù)學(xué)研究所建所10周年大會(huì)(已修改)
2025-08-07 12:40 本頁面
【正文】 AbstractsThe 10th Anniversary (19942004) Conference for the Institute of Mathematics, ECNUamp。International Conference on Complex Geometry and Related Theories華東師范大學(xué)數(shù)學(xué)研究所建所10周年大會(huì)暨復(fù)幾何及相關(guān)的數(shù)學(xué)理論國際會(huì)議ABSTRACTSJune 21 – 25, 2004East China Normal University華東師范大學(xué)Shanghai, ChinaShingTung Yau (丘成桐，Harvard University)Title: Brief history on plex manifolds and some future directionsRoger W. Brockett (Harvard University)Title: A New Formulation of the Optimal Control Problem Involving Implementation Cost Although much of the literature on automatic control is concerned with definitions of optimality relating to the shape of trajectories and the magnitude of the control required to generate them, it often happens that costs related to the implementation of the control are more significant than the cost associated with imperfect trajectories. In biological motor control, for example, there are many situations in which imprecise control is virtually as good as precise control。 the more important objective is to find a control law that can be implemented without diverting attention from the other tasks which are more pressing. This raises a question that has received little notice until now, ``How can the cost of implementation be taken into account when formulating an optimal control problem?`` Starting from the point of view that the easiest control law to implement is a constant, we develop a family of precise optimization problems whose solution lead to controls that require less frequent updating and are more robust with respect to small changes in the data. These considerations suggest a mathematical approach leading to a measure of the attention required to implement a given control law.Fabrizio Catanese (University of Bayreuth)Title: Lefschetz fibrations in the differentiable and symplectic category and applications to Moduli spaces of algebraic surfacesIn the talk I will report about joint work with B. Wajnryb. First on the results which we already obtained, showing that even in the case of simply connected minimal algebraic surfaces of general type, deformation and differentiable equivalence do not coincide.Exhibiting the simple families of abc surfaces which are not deformation equivalent, and proving their diffeomorphism, we get a counterexample to a weaker form of the speculation DEF = DIFF of R. Friedman and J. Morgan, ., in the case where (by M. Freedman39。s theorem) the topological type is pletely determined by the numerical invariants of the surface.The methods of proof are rather general, but if we want to investigate the natural symplectic structures associated to the canonical class, the question of symplectic equivalence bees more subtle in the 1connected case. I will explain also work in progress on this second question, especially some beautiful geometry of discriminant curves.Yongchuan Chen (陳永川，Nankai University)Title: Nanhua Xi (席南華，Chinese Academy of Sciences)Title: Based rings and Representations of affine Hecke algebrasWe shall give an answer to a question of Lusztig on representations of affine Hecke algebras, by using the based ring of an affine Weyl group.YumTong Siu (蕭蔭棠，Harvard University)Title: Regularity problems of the problemWe will discuss results and problems related to the regularity of the problem for weakly pseudoconvex domains such as the touching orders of local holomorphic curves, Lie brackets of plexvalued vector fields, subellipticity, hypoellipticity, the Frobeniu
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