Deformations of Complex Structures
Deformations of Complex Structures
批准号:
9800924
负责人:
Christopher Bishop
金额:
$23.48万
依托单位:
依托单位国家:
美国
项目类别:
Continuing Grant
财政年份:
1998
资助国家:
美国
项目状态:
已结题
起止时间:
1998-06-15 至 2002-05-31
中文摘要
点击翻译按钮获取中文摘要
英文摘要
Prof. Bishop will investigate several aspects of geometry and analysis related to non-smooth objects such as limit sets of Kleinian groups, Brownian motion and quasi-conformal mappings. Among the specific goals are to extend his earlier application of harmonic analysis and heat kernel techniques to compute the exact size (in terms of Hausdorff measures) of the limit sets of Kleinian groups to new examples (e.g., manifolds with thin parts) and new sets (the conical limit set, the set of escaping geodesics,...). He will also attempt to extend Bowen's famous dichotomy to all divergence type Fuchsian groups, extending work of Sullivan, Astala, Zinsmeister, Jones and himself. Part of this is to further study the ``beta''s, a technical measure of how close a set is to a line segment at different scales, which is closely related to the study of the traveling salesman problem. He will also continue his work investigating the removable and non-removable sets for quasi-conformal mappings, geometric properties of Brownian motion, and other geometric-analytic questions in classical complex analysis.The proposal deals with a variety of geometric questions which are united by a desire to understand traditional concepts and calculations (e.g. compute the area of a region) in non-traditional and highly non-smooth cases. This is motivated by (at least) two points of view. First, a better understanding of the classical case can be obtained by seeing how it succeeds or fails in a more general setting; even the failures lead to new, interesting phenomena to investigate. Second, many applications of mathematics (polymers, fractures, shock waves, wavelet analysis, crystal growth,...) involve highly irregular and fractal objects, and we need to understand and calculate with such objects the way we have always done with much smoother quantities. For example, Brownian motion is a mathematical object which models random movement and is of tremendous intrinsic interest, as well as being fundamental to understanding many other random processes (e.g., shapes of long polymers chains, growth of crystals by random accretion, ...). However, Brownian motion is an extremely non-smooth process and various simple geometric questions about its random paths are still unknown. Another example is with the Kleinian groups mentioned above. These are symmetries in non-Euclidean geometry; as such, they are fundamental objects in topology and have been an area of intense investigation for many years. They can be associated with certain fractal objects (the limit sets) involving non-linear rescalings, where the non-linearity is of a very special type, and present a theoretical stepping stone between self-similar sets with linear rescalings (which are fairly well understood) and much more complicated rescalings found in rational dynamics and chaos theory.
期刊论文(0)
专著(0)
科研奖励(0)
会议论文
Quasiconformal analysis, optimal triangulations and fractal geometry
-
批准号:2303987
-
项目类别:Standard Grant
-
资助金额:$41.79万
-
财政年份:2023
-
负责人:Christopher Bishop
-
依托单位:
I-Corps: Repurposing Serotoninergic Compounds for Improved Treatment of Parkinson's Disease
-
批准号:2148598
-
项目类别:Standard Grant
-
资助金额:$5.0万
-
财政年份:2021
-
负责人:Christopher Bishop
-
依托单位:
Quasiconformal Constructions in Analysis and Dynamics
-
批准号:1906259
-
项目类别:Continuing Grant
-
资助金额:$26.91万
-
财政年份:2019
-
负责人:Christopher Bishop
-
依托单位:
Geometric Problems in Conformal Analysis, Dynamics, and Probability
-
批准号:1608577
-
项目类别:Continuing Grant
-
资助金额:$22.16万
-
财政年份:2016
-
负责人:Christopher Bishop
-
依托单位:
Quasiconformal methods in analysis, geometry and dynamics
-
批准号:1305233
-
项目类别:Continuing Grant
-
资助金额:$17.61万
-
财政年份:2013
-
负责人:Christopher Bishop
-
依托单位:
Analysis of conformal and quasiconformal maps
-
批准号:1006309
-
项目类别:Standard Grant
-
资助金额:$20.04万
-
财政年份:2010
-
负责人:Christopher Bishop
-
依托单位:
Computational and Conformal Geometry
-
批准号:0705455
-
项目类别:Continuing Grant
-
资助金额:$18.0万
-
财政年份:2007
-
负责人:Christopher Bishop
-
依托单位:
Geometry of Conformal and Quasiconformal Mappings
-
批准号:0405578
-
项目类别:Standard Grant
-
资助金额:$20.0万
-
财政年份:2004
-
负责人:Christopher Bishop
-
依托单位:
Geometry of Conformal and Quasiconformal Mappings
-
批准号:0103626
-
项目类别:Continuing Grant
-
资助金额:$17.64万
-
财政年份:2001
-
负责人:Christopher Bishop
-
依托单位:
Mathematical Sciences: Postdoctoral Research Fellowship
-
批准号:8705957
-
项目类别:Fellowship Award
-
资助金额:$7.41万
-
财政年份:1987
-
负责人:Christopher Bishop
-
依托单位:
国内基金
海外基金
登录
查看更多内容
TPLATE Complex通过胞吞调控CLV3-CLAVATA多肽信号模块维持干细胞稳态的分子机制研究
-
批准号:32370337
-
项目类别:面上项目
-
资助金额:50万元
-
批准年份:2023
-
负责人:王杰
-
依托单位:
二甲双胍对于模型蛋白、γ-secretase、Complex I自由能曲面的影响
-
批准号:--
-
项目类别:青年科学基金项目
-
资助金额:30万元
-
批准年份:2022
-
负责人:郭子龙
-
依托单位:
高脂饮食损伤巨噬细胞ndufs4表达激活Complex I/mROS/HIF-1通路参与溃疡性结肠炎研究
-
批准号:--
-
项目类别:青年科学基金项目
-
资助金额:30万元
-
批准年份:2022
-
负责人:赵锐
-
依托单位:
线粒体参与呼吸中枢pre-Bötzinger complex呼吸可塑性调控的机制研究
-
批准号:31971055
-
项目类别:面上项目
-
资助金额:58.0万元
-
批准年份:2019
-
负责人:刘莹莹
-
依托单位:
北温带中华蹄盖蕨复合体Athyrium sinense complex的物种分化
-
批准号:31872651
-
项目类别:面上项目
-
资助金额:60.0万元
-
批准年份:2018
-
负责人:张宪春
-
依托单位:
边缘鳞盖蕨复合体种 (Microlepia marginata complex) 的网状进化及物种形成研究
-
批准号:31860044
-
项目类别:地区科学基金项目
-
资助金额:37.0万元
-
批准年份:2018
-
负责人:王任翔
-
依托单位:
益气通络颗粒及主要单体通过调节cAMP/PKA/Complex I通路治疗气虚血瘀证脑梗死的机制研究
-
批准号:81703747
-
项目类别:青年科学基金项目
-
资助金额:20.0万元
-
批准年份:2017
-
负责人:薛冰洁
-
依托单位:
生物钟转录抑制复合体 Evening Complex 调控茉莉酸诱导叶片衰老的分子机制研究
-
批准号:31670290
-
项目类别:面上项目
-
资助金额:62.0万元
-
批准年份:2016
-
负责人:张媛媛
-
依托单位:
延伸子复合物(Elongator complex)的翻译调控作用
-
批准号:31360023
-
项目类别:地区科学基金项目
-
资助金额:51.0万元
-
批准年份:2013
-
负责人:黄波
-
依托单位:
Complex I 基因变异与寿命的关联及其作用机制的研究
-
批准号:81370445
-
项目类别:面上项目
-
资助金额:70.0万元
-
批准年份:2013
-
负责人:杨泽
-
依托单位: