Groups, Arithmetic, and Monodromy
群、算术和单数
基本信息
- 批准号:1101424
- 负责人:
- 金额:$ 15.88万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Continuing Grant
- 财政年份:2011
- 资助国家:美国
- 起止时间:2011-07-01 至 2017-06-30
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
I propose to study the monodromy of Galois representations arising from cohomology, both to prove that it is generally as large as possible, and to use it to attack the inverse Galois problem for l-adic Lie groups. Such inverse problems are connected with deformation theory of Galois representations, and I propose also to investigate analogous problems in the deformation theory of representations of discrete 1-relator groups. Such representations are parametrized by the identity fiber of the word map associated to a given relation, and I propose further to study the geometry of such word maps more broadly, with applications to group theory. In a different direction, I intend to study the inverse Galois problem for Mordell-Weil groups and related questions in field arithmetic.Groups are the possible types of symmetry in pure and applied mathematics. In nature, groups very often arise in the study of "monodromy". The idea of monodromy gives one a common framework for considering a wide range of apparently quite different questions. For example: what happens to the solutions of a differential equation as they are followed around singular points back to their starting points? What are the possible symmetries of the number systems generated by coordinates of special points on curves? What are the possible states of a quantum computer obtainable by a sequence of machine operations? I propose to study groups, both to better understand their internal structure and, in the case of monodromy groups, to gain insight into the geometries and number systems which give rise to them.
我建议研究由上同调引起的伽罗瓦表示的单性,既证明它一般是尽可能大的,又利用它来解决l进李群的伽罗瓦逆问题。这类反问题与伽罗瓦表示的变形理论有关,我也建议研究离散1-相关群表示的变形理论中的类似问题。这种表示是由与给定关系相关的词映射的同一性纤维参数化的,我建议进一步研究这种词映射的几何更广泛,并应用于群论。在另一个方向上,我打算研究modell - weil群的反伽罗瓦问题和场算法中的相关问题。群是纯数学和应用数学中对称的可能类型。在自然界中,群体经常出现在对“单一性”的研究中。单一性的概念给人们提供了一个共同的框架来考虑范围广泛的、明显不同的问题。例如:当微分方程的解绕着奇异点回到它们的起始点时会发生什么?曲线上特殊点的坐标所产生的数字系统的可能对称性是什么?通过一系列机器操作可以获得的量子计算机的可能状态是什么?我建议学习群体,一方面是为了更好地理解它们的内部结构,另一方面,在单群的情况下,是为了深入了解产生它们的几何形状和数字系统。
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)
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Michael Larsen其他文献
Randomized sham-controlled trial of the 6-month swallowable gas-filled intragastric balloon system for weight loss.
对为期 6 个月的可吞咽充气胃内气球系统进行减肥的随机假对照试验。
- DOI:
- 发表时间:
2018 - 期刊:
- 影响因子:3.1
- 作者:
Shelby Sullivan;J. Swain;G. Woodman;S. Edmundowicz;T. Hassanein;V. Shayani;John Fang;M. Noar;G. Eid;Wayne J. English;N. Tariq;Michael Larsen;S. Jonnalagadda;D. Riff;J. Ponce;D. Early;E. Volckmann;A. Ibele;Matthew D. Spann;K. Krishnan;J. Bucobo;A. Pryor - 通讯作者:
A. Pryor
Petechial hemorrhages of the tympanic membrane in attempted suicide by hanging: A case report
- DOI:
10.1016/j.jflm.2012.05.007 - 发表时间:
2013-02-01 - 期刊:
- 影响因子:
- 作者:
Eva Rye Rasmussen;Per Leganger Larsen;Kjeld Andersen;Michael Larsen;Klaus Qvortrup;Hans Petter Hougen - 通讯作者:
Hans Petter Hougen
DIAGNOSTIC VALUE AND COST OF MRCP AND EUS FOR THE EVALUATION OF CHOLEDOCHOLITHIASIS: A RETROSPECTIVE COHORT ANALYSIS
- DOI:
10.1016/j.gie.2024.04.1108 - 发表时间:
2024-06-01 - 期刊:
- 影响因子:
- 作者:
Karena Puldon;Logan Pierce;Patrick Avila;Michael Larsen;Sun-Chuan Dai;Mustafa Arain;Abdul Kouanda - 通讯作者:
Abdul Kouanda
Tensor product Markov chains and Weil representations
张量积马尔可夫链与韦伊表示
- DOI:
10.1016/j.jalgebra.2025.05.041 - 发表时间:
2025-11-15 - 期刊:
- 影响因子:0.800
- 作者:
Jason Fulman;Michael Larsen;Pham Huu Tiep - 通讯作者:
Pham Huu Tiep
On The Correlation Of Binary M-sequences
- DOI:
10.1023/a:1008383811226 - 发表时间:
1999-01-01 - 期刊:
- 影响因子:1.200
- 作者:
John Friedlander;Michael Larsen;Daniel Lieman;Igor Shparlinski - 通讯作者:
Igor Shparlinski
Michael Larsen的其他文献
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{{ truncateString('Michael Larsen', 18)}}的其他基金
RUI: Dynamic Guanidine-based Polymer Networks
RUI:动态胍基聚合物网络
- 批准号:
2105149 - 财政年份:2021
- 资助金额:
$ 15.88万 - 项目类别:
Continuing Grant
Collaborative Research to Explore the Spatial/Temporal Statistical-Physical Structures of Rain in the Vertical Plane
探索垂直平面降雨时空统计物理结构的合作研究
- 批准号:
2001490 - 财政年份:2020
- 资助金额:
$ 15.88万 - 项目类别:
Standard Grant
Developing a Life Sciences Workforce with Strong Quantitative Skills
培养具有强大定量技能的生命科学员工队伍
- 批准号:
1742241 - 财政年份:2018
- 资助金额:
$ 15.88万 - 项目类别:
Standard Grant
Collaborative Research: The Relationship of the Spatial/Temporal Variability of Rain to Scaling
合作研究:降雨的时空变化与尺度的关系
- 批准号:
1823334 - 财政年份:2018
- 资助金额:
$ 15.88万 - 项目类别:
Standard Grant
Collaborative Research: The Meteorological Variability of the Two Dimensional/Temporal Structures of Drop Size Distributions and Rain
合作研究:雨滴尺寸分布和降雨的二维/时间结构的气象变化
- 批准号:
1532977 - 财政年份:2015
- 资助金额:
$ 15.88万 - 项目类别:
Continuing Grant
Collaborative Research: Characterization of the Two-dimensional/Temporal Mosaic of Drop Size Distributions and Spatial Variability (Structure) in Rain
合作研究:雨中液滴尺寸分布和空间变化(结构)的二维/时间镶嵌特征
- 批准号:
1230240 - 财政年份:2012
- 资助金额:
$ 15.88万 - 项目类别:
Continuing Grant
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