Resolution of Singularities and its applications. Analysis on and geometry of singular spaces.
奇点的解决及其应用。
基本信息
- 批准号:8949-2013
- 负责人:
- 金额:$ 2.77万
- 依托单位:
- 依托单位国家:加拿大
- 项目类别:Discovery Grants Program - Individual
- 财政年份:2016
- 资助国家:加拿大
- 起止时间:2016-01-01 至 2017-12-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
Singularities express irregularities of form in many branches of mathematics in a way similar to what it means in an everyday language and are a basic object of study in most of the mathematics and its applications. The important features of form are often concentrated at singularities. The objective of my research is to find links between the information encoded in the geometry of and the analysis on singular objects.This led me to a discovery of fundamental links between algebraic, analytic and geometric aspects of singularities, particularly in solutions of longstanding problems posed by Whitney, Thom and Hironaka - the originators of the singularity theories in geometry and algebra. This also led me to an extension of classical Sobolev-Nirenberg and Bernstein-Markov inequalities to a singular setting, and to a discovery of `tame' subanalytic sets on which one can do classical local analysis.
奇点在许多数学分支中表达形式的不规则性,其方式类似于它在日常语言中的含义,并且是大多数数学及其应用中的基本研究对象。形式的重要特征往往集中在奇点上。我的研究目的是找到奇点的几何学和分析中所编码的信息之间的联系。这使我发现了奇点的代数、解析和几何方面之间的基本联系,特别是在解决惠特尼、托姆和平中--几何和代数奇点理论的创始人--提出的长期存在的问题时。这也使我将经典的Sobolev-Nirenberg和Bernstein-马尔可夫不等式推广到奇异环境,并发现了可以在其上进行经典局部分析的“驯服”次分析集。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
数据更新时间:{{ journalArticles.updateTime }}
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
数据更新时间:{{ journalArticles.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ monograph.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ sciAawards.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ conferencePapers.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ patent.updateTime }}
Milman, Pierre其他文献
Milman, Pierre的其他文献
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
{{ truncateString('Milman, Pierre', 18)}}的其他基金
Desingularization and applications. Analysis on and Geometry of singular spaces
去奇异化和应用。
- 批准号:
RGPIN-2018-04445 - 财政年份:2022
- 资助金额:
$ 2.77万 - 项目类别:
Discovery Grants Program - Individual
Desingularization and applications. Analysis on and Geometry of singular spaces
去奇异化和应用。
- 批准号:
RGPIN-2018-04445 - 财政年份:2021
- 资助金额:
$ 2.77万 - 项目类别:
Discovery Grants Program - Individual
Desingularization and applications. Analysis on and Geometry of singular spaces
去奇异化和应用。
- 批准号:
RGPIN-2018-04445 - 财政年份:2020
- 资助金额:
$ 2.77万 - 项目类别:
Discovery Grants Program - Individual
Desingularization and applications. Analysis on and Geometry of singular spaces
去奇异化和应用。
- 批准号:
RGPIN-2018-04445 - 财政年份:2019
- 资助金额:
$ 2.77万 - 项目类别:
Discovery Grants Program - Individual
Desingularization and applications. Analysis on and Geometry of singular spaces
去奇异化和应用。
- 批准号:
RGPIN-2018-04445 - 财政年份:2018
- 资助金额:
$ 2.77万 - 项目类别:
Discovery Grants Program - Individual
Resolution of Singularities and its applications. Analysis on and geometry of singular spaces.
奇点的解决及其应用。
- 批准号:
8949-2013 - 财政年份:2017
- 资助金额:
$ 2.77万 - 项目类别:
Discovery Grants Program - Individual
Resolution of Singularities and its applications. Analysis on and geometry of singular spaces.
奇点的解决及其应用。
- 批准号:
8949-2013 - 财政年份:2015
- 资助金额:
$ 2.77万 - 项目类别:
Discovery Grants Program - Individual
Resolution of Singularities and its applications. Analysis on and geometry of singular spaces.
奇点的解决及其应用。
- 批准号:
8949-2013 - 财政年份:2014
- 资助金额:
$ 2.77万 - 项目类别:
Discovery Grants Program - Individual
Resolution of Singularities and its applications. Analysis on and geometry of singular spaces.
奇点的解决及其应用。
- 批准号:
8949-2013 - 财政年份:2013
- 资助金额:
$ 2.77万 - 项目类别:
Discovery Grants Program - Individual
Analysis on and geometry of singular spaces towards a geometric desingularization
奇异空间的分析和几何走向几何去奇异化
- 批准号:
8949-2008 - 财政年份:2012
- 资助金额:
$ 2.77万 - 项目类别:
Discovery Grants Program - Individual
相似海外基金
Automatic classification and recognition of singularities and its application
奇点自动分类识别及其应用
- 批准号:
23K03123 - 财政年份:2023
- 资助金额:
$ 2.77万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Singularity theory in mixed characteristic and its applications to the theory of F-singularities and birational geometry
混合特性奇异性理论及其在F-奇异性和双有理几何理论中的应用
- 批准号:
22H01112 - 财政年份:2022
- 资助金额:
$ 2.77万 - 项目类别:
Grant-in-Aid for Scientific Research (B)
Differential geometrey of singularities and its applications
奇点微分几何及其应用
- 批准号:
21H00981 - 财政年份:2021
- 资助金额:
$ 2.77万 - 项目类别:
Grant-in-Aid for Scientific Research (B)
Geometric equivalence among singularities and its applications
奇点间的几何等价及其应用
- 批准号:
20K03599 - 财政年份:2020
- 资助金额:
$ 2.77万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Resolution of Singularities and its applications. Analysis on and geometry of singular spaces.
奇点的解决及其应用。
- 批准号:
8949-2013 - 财政年份:2017
- 资助金额:
$ 2.77万 - 项目类别:
Discovery Grants Program - Individual
Resolution of singularities by using Newton polyhedra and its application to analysis
牛顿多面体奇点解析及其在分析中的应用
- 批准号:
15K04932 - 财政年份:2015
- 资助金额:
$ 2.77万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Resolution of Singularities and its applications. Analysis on and geometry of singular spaces.
奇点的解决及其应用。
- 批准号:
8949-2013 - 财政年份:2015
- 资助金额:
$ 2.77万 - 项目类别:
Discovery Grants Program - Individual
Resolution of Singularities and its applications. Analysis on and geometry of singular spaces.
奇点的解决及其应用。
- 批准号:
8949-2013 - 财政年份:2014
- 资助金额:
$ 2.77万 - 项目类别:
Discovery Grants Program - Individual
Resolution of Singularities and its applications. Analysis on and geometry of singular spaces.
奇点的解决及其应用。
- 批准号:
8949-2013 - 财政年份:2013
- 资助金额:
$ 2.77万 - 项目类别:
Discovery Grants Program - Individual
Analysis of real singularities and its application to mathematical information
实奇点分析及其在数学信息中的应用
- 批准号:
23740094 - 财政年份:2011
- 资助金额:
$ 2.77万 - 项目类别:
Grant-in-Aid for Young Scientists (B)