FRG: Collaborative Research: Algebraic Geometry and Singularities in Positive and Mixed Characteristic

FRG:合作研究:代数几何和正特征和混合特征中的奇点

基本信息

项目摘要

Algebraic Geometry studies algebraic varieties which are geometric objects defined by polynomial equations. One of the most natural problems in this area is to understand the singularities that naturally occur when considering algebraic varieties and how these singularities influence the global geometry of algebraic varieties. In recent years there have been a number of breakthroughs, especially in the case where we consider solutions over the complex numbers. At the same time new techniques and approaches have emerged for studying solutions in positive and mixed characteristics. The primary goal of this collaborative project is to advance and unify these ideas to further understand and solve some of the most challenging programs in both local and global algebraic geometry. In addition the project provides research training opportunities for graduate students. The PIs will investigate singularities in positive and mixed characteristics by using a variety of techniques including those arising from the minimal model program, from the theory of F-singularities, and from Scholze's work on perfectoid algebras and spaces. The PIs will also organize workshops, a summer school and a conference, aimed at training young researchers in this area, disseminating recent results and facilitating further advances and breakthroughs.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
代数几何学研究的是代数簇,它是由多项式方程定义的几何对象。在这一领域最自然的问题之一是理解奇异性,自然发生时,考虑代数簇和这些奇异性如何影响全球几何的代数簇。近年来有一些突破,特别是在我们考虑复数的解决方案的情况下。与此同时,出现了新的技术和方法来研究解决方案的积极和混合的特点。这个合作项目的主要目标是推进和统一这些想法,以进一步理解和解决局部和全局代数几何中一些最具挑战性的程序。此外,该项目还为研究生提供研究培训机会。该PI将调查奇点的积极和混合的特点,通过使用各种技术,包括那些所产生的最小模型计划,从理论的F-奇点,并从Scholze的工作perfectoid代数和空间。该奖项反映了NSF的法定使命,并通过使用基金会的知识价值和更广泛的影响审查标准进行评估,被认为值得支持。

项目成果

期刊论文数量(1)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
The six functors for Zariski-constructible sheaves in rigid geometry
刚性几何中 Zariski 可构造滑轮的六个函子
  • DOI:
    10.1112/s0010437x22007291
  • 发表时间:
    2022
  • 期刊:
  • 影响因子:
    1.8
  • 作者:
    Bhatt, Bhargav;Hansen, David
  • 通讯作者:
    Hansen, David
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Karen Smith其他文献

『功利主義と政策思想の展開』第3章「シジウィック・ムーア・ピグー-功利主義・正義の観点から-」(音無通宏編)
《功利主义与政策思想的发展》第3章《西奇威克、摩尔和庇古——从功利主义和正义的视角》(音无道弘主编)
  • DOI:
  • 发表时间:
    2011
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Chulhee Kang;Femida Handy;Lesley Hustinx;Ram Cnaan;Jeffrey L.Brudney;Debbie Haski-Leventhal;Kirsten Holmes;Lucas Meijs;Anne Birgitta Pessi;Bhagyashree Ranade;Karen Smith;Naoto Yamauchi;Sinisa Zrinscak;山崎聡
  • 通讯作者:
    山崎聡
Differentiation of confirmed major trauma patients and potential major trauma patients using pre-hospital trauma triage criteria.
使用院前创伤分诊标准区分已确诊的重大创伤患者和潜在的重大创伤患者。
  • DOI:
    10.1016/j.injury.2010.03.035
  • 发表时间:
    2011
  • 期刊:
  • 影响因子:
    2.5
  • 作者:
    S. Cox;Karen Smith;A. Currell;L. Harriss;B. Barger;P. Cameron
  • 通讯作者:
    P. Cameron
Testing for Drugs of Abuse in Children and Adolescents: Addendum—Testing in Schools and at Home
儿童和青少年滥用药物检测:附录 — 在学校和家庭进行检测
  • DOI:
    10.1542/peds.2006-3688
  • 发表时间:
    2007
  • 期刊:
  • 影响因子:
    8
  • 作者:
    Alain Joffe;Marylou Behnke;J. Knight;P. Kokotailo;Tammy H. Sims;Janet Williams;J. Kulig;Deborah Simkin;Linn Goldberg;Sharon Levy;Karen Smith;Robert D. Murray;B. L. Frankowski;R. Gereige;C. Mears;Michele M. Roland;Thomas L. Young;Linda M. Grant;Daniel Hyman;Harold Magalnick;George J. Monteverdi;Evan G. Pattishall;Nancy LaCursia;Donna Mazyck;Mary E. Vernon;Robin Wallace;Madra Guinn
  • 通讯作者:
    Madra Guinn
Residential aged care homes: Why do they call ‘000’? A study of the emergency prehospital care of older people living in residential aged care homes
居家养老院:为何将其称为“000”?对居家养老院老年人的院前紧急护理的研究
  • DOI:
    10.1111/1742-6723.13650
  • 发表时间:
    2020
  • 期刊:
  • 影响因子:
    2.3
  • 作者:
    R. Dwyer;B. Gabbe;T. Tran;Karen Smith;J. Lowthian
  • 通讯作者:
    J. Lowthian
Energy in Schools: Empowering Children to Deliver Behavioural Change for Sustainability
学校活力:赋予儿童行为改变以实现可持续发展的能力

Karen Smith的其他文献

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{{ truncateString('Karen Smith', 18)}}的其他基金

Studies in Commutative Algebra and Algebraic Geometry
交换代数和代数几何研究
  • 批准号:
    2200501
  • 财政年份:
    2022
  • 资助金额:
    $ 40.25万
  • 项目类别:
    Continuing Grant
Commutative Algebra: Extremal Singularities in Prime Characteristic
交换代数:素数特征中的极值奇点
  • 批准号:
    2101075
  • 财政年份:
    2021
  • 资助金额:
    $ 40.25万
  • 项目类别:
    Continuing Grant
Commutative Algebra: F-Regularity in Algebraic Geometry and Non-Commutative Algebra
交换代数:代数几何和非交换代数中的 F 正则性
  • 批准号:
    1801697
  • 财政年份:
    2018
  • 资助金额:
    $ 40.25万
  • 项目类别:
    Continuing Grant
Algorithm Development For Reconstruction Of Design Elements
设计元素重构的算法开发
  • 批准号:
    1658987
  • 财政年份:
    2017
  • 资助金额:
    $ 40.25万
  • 项目类别:
    Standard Grant
The Impact of the Stratosphere on Arctic Climate
平流层对北极气候的影响
  • 批准号:
    1603350
  • 财政年份:
    2016
  • 资助金额:
    $ 40.25万
  • 项目类别:
    Standard Grant
Commutative Algebra: Frobenius in Geometry and Combinatorics
交换代数:几何和组合学中的弗罗贝尼乌斯
  • 批准号:
    1501625
  • 财政年份:
    2015
  • 资助金额:
    $ 40.25万
  • 项目类别:
    Continuing Grant
EMSW21-RTG: Developing American Research Leadership in Algebraic Geometry and its Boundaries
EMSW21-RTG:发展美国在代数几何及其边界方面的研究领导地位
  • 批准号:
    0943832
  • 财政年份:
    2010
  • 资助金额:
    $ 40.25万
  • 项目类别:
    Continuing Grant
Bringing Frobenius to Bear on Birational Algebraic Geometry
将弗罗贝尼乌斯应用于双有理代数几何
  • 批准号:
    1001764
  • 财政年份:
    2010
  • 资助金额:
    $ 40.25万
  • 项目类别:
    Continuing Grant
Commutative Algebra and its Interactions, July 31 - August 3, 2008
交换代数及其相互作用,2008年7月31日至8月3日
  • 批准号:
    0810844
  • 财政年份:
    2008
  • 资助金额:
    $ 40.25万
  • 项目类别:
    Standard Grant
Noncommutative Geometry and Cherednik Algebras
非交换几何和切里德尼克代数
  • 批准号:
    0555750
  • 财政年份:
    2006
  • 资助金额:
    $ 40.25万
  • 项目类别:
    Continuing Grant

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