Algebraic combinatorics of graphs and matroids
图和拟阵的代数组合
基本信息
- 批准号:105392-2013
- 负责人:
- 金额:$ 1.09万
- 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:2017
- 资助国家:加拿大
- 起止时间:2017-01-01 至 2018-12-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
The theory of electrical networks provides a natural and significant starting point from which to begin investigating the connections among mathematical physics, complex analysis, and enumeration problems in graph theory. The origins of this theory are in the 19th century -- with pioneers like Cayley, Kirchhoff, Maxwell, and Rayleigh -- but a modern perspective on the subject has led to deep new insights in recent decades. The 19th century material is now very well understood, and the current unifying theme is to discover the degree to which these old results can be extended to more general situations, or to more precise statements. The modern perspective begins with the Potts model in the 1950s, the dimer model defined by Heilmann and Lieb in the 1970s, and the random cluster model defined by Fortuin, Kasteleyn, and Ginibre in the 1970s. These are mathematical abstractions of physical systems such as adhesion, crystallization, or magnetization, and the theory of electrical networks is recovered as a simple special case. Of central interest is the question of phase transitions -- as the temperature or pressure or other parameters change, does the physical behaviour of the system undergo a shift into a qualitatively different state? This is analogous to the freezing or boiling of water, but the goal is to understand the phenomena quantitatively at a microscopic scale. Correlation inequalities are key ingredients in the analysis of phase transitions -- these measure the extent to which certain events are likely to occur together, or to interfere with one another. The main direction of my research is to establish negative correlation inequalities for the random cluster model, complementing positive correlation inequalities proved by Fortuin, Kasteleyn, and Ginibre. Along with their physical interpretation, such inequalities also have applications in combinatorial enumeration and probability theory. The techniques involved in the proof of such inequalities range from classical complex analysis and linear algebra to very recent results in the combinatorics of graphs and matroids. Progress on these questions will advance our understanding of the properties of mathematical models of various physical phenomena.
电子网络理论为开始研究图论中的数学物理、复杂分析和枚举问题之间的联系提供了一个自然而重要的起点。这一理论起源于19世纪,由Cayley、Kirchhoff、Maxwell和Rayleigh等先驱者提出,但近几十年来,对这一主题的现代观点产生了深刻的新见解。19世纪的材料现在已经被很好地理解了,当前的统一主题是发现这些旧的结果可以在多大程度上推广到更一般的情况,或者更精确的陈述。现代视角始于20世纪50年代的Potts模型,70年代由Heilmann和Lieb定义的二聚体模型,以及20世纪70年代由Fortuin、Kasteleyn和Ginibre定义的随机集群模型。这些是物理系统的数学抽象,如粘附、结晶或磁化,电网络理论被恢复为一个简单的特殊情况。最重要的是相变问题——随着温度、压力或其他参数的变化,系统的物理行为是否会转变为一种性质不同的状态?这类似于水的冻结或沸腾,但目标是在微观尺度上定量地理解这些现象。相关不平等是相变分析的关键因素——它们衡量某些事件可能同时发生或相互干扰的程度。我的主要研究方向是建立随机聚类模型的负相关不等式,补充Fortuin、Kasteleyn和Ginibre证明的正相关不等式。除了它们的物理解释,这些不等式在组合枚举和概率论中也有应用。证明这些不等式所涉及的技术范围从经典的复分析和线性代数到最近的图和拟阵组合学的结果。在这些问题上的进展将促进我们对各种物理现象的数学模型的性质的理解。
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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Wagner, David其他文献
Hopper: Modeling and Detecting Lateral Movement
料斗:建模和检测横向运动
- DOI:
- 发表时间:
2021 - 期刊:
- 影响因子:0
- 作者:
Ho, Grant;Dhiman, Mayank;Akhawe, Devdatta;Paxson, Vern;Savage, Stefan;Voelker, Geoffrey M.;Wagner, David - 通讯作者:
Wagner, David
Situated Perspectives on Creating Mathematics Tasks for Peace and Sustainability
- DOI:
10.1007/s42330-020-00083-w - 发表时间:
2020-03-25 - 期刊:
- 影响因子:1.5
- 作者:
Yaro, Kwesi;Amoah, Emmanuel;Wagner, David - 通讯作者:
Wagner, David
Simultaneous noninvasive recording of skin sympathetic nerve activity and electrocardiogram.
- DOI:
10.1016/j.hrthm.2016.09.019 - 发表时间:
2017-01 - 期刊:
- 影响因子:5.5
- 作者:
Doytchinova, Anisiia;Hassel, Jonathan L.;Yuan, Yuan;Lin, Hongbo;Yin, Dechun;Adams, David;Straka, Susan;Wright, Keith;Smith, Kimberly;Wagner, David;Shen, Changyu;Salanova, Vicenta;Meshberger, Chad;Chen, Lan S.;Kincaid, John C.;Coffey, Arthur C.;Wu, Gang;Li, Yan;Kovacs, Richard J.;Everett, Thomas H.;Victor, Ronald;Cha, Yong-Mei;Lin, Shien-Fong;Chen, Peng-Sheng - 通讯作者:
Chen, Peng-Sheng
Privacy Controls for Always-Listening Devices
始终监听设备的隐私控制
- DOI:
10.1145/3368860.3368867 - 发表时间:
2019 - 期刊:
- 影响因子:0
- 作者:
Malkin, Nathan;Egelman, Serge;Wagner, David - 通讯作者:
Wagner, David
Appraising lexical bundles in mathematics classroom discourse: obligation and choice
- DOI:
10.1007/s10649-010-9240-y - 发表时间:
2010-09-01 - 期刊:
- 影响因子:3.2
- 作者:
Herbel-Eisenmann, Beth;Wagner, David - 通讯作者:
Wagner, David
Wagner, David的其他文献
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{{ truncateString('Wagner, David', 18)}}的其他基金
Algebraic combinatorics of graphs and matroids
图和拟阵的代数组合
- 批准号:
105392-2013 - 财政年份:2015
- 资助金额:
$ 1.09万 - 项目类别:
Discovery Grants Program - Individual
Algebraic combinatorics of graphs and matroids
图和拟阵的代数组合
- 批准号:
105392-2013 - 财政年份:2014
- 资助金额:
$ 1.09万 - 项目类别:
Discovery Grants Program - Individual
Algebraic combinatorics of graphs and matroids
图和拟阵的代数组合
- 批准号:
105392-2013 - 财政年份:2013
- 资助金额:
$ 1.09万 - 项目类别:
Discovery Grants Program - Individual
Negative correlations in combinatorics and statistical mechanics
组合数学和统计力学中的负相关
- 批准号:
105392-2007 - 财政年份:2011
- 资助金额:
$ 1.09万 - 项目类别:
Discovery Grants Program - Individual
Negative correlations in combinatorics and statistical mechanics
组合数学和统计力学中的负相关
- 批准号:
105392-2007 - 财政年份:2010
- 资助金额:
$ 1.09万 - 项目类别:
Discovery Grants Program - Individual
Negative correlations in combinatorics and statistical mechanics
组合数学和统计力学中的负相关
- 批准号:
105392-2007 - 财政年份:2009
- 资助金额:
$ 1.09万 - 项目类别:
Discovery Grants Program - Individual
Negative correlations in combinatorics and statistical mechanics
组合数学和统计力学中的负相关
- 批准号:
105392-2007 - 财政年份:2008
- 资助金额:
$ 1.09万 - 项目类别:
Discovery Grants Program - Individual
Negative correlations in combinatorics and statistical mechanics
组合数学和统计力学中的负相关
- 批准号:
105392-2007 - 财政年份:2007
- 资助金额:
$ 1.09万 - 项目类别:
Discovery Grants Program - Individual
Enumerative and algebraic combinatorics of graphs and partial orders
图和偏序的枚举和代数组合
- 批准号:
105392-2002 - 财政年份:2006
- 资助金额:
$ 1.09万 - 项目类别:
Discovery Grants Program - Individual
Enumerative and algebraic combinatorics of graphs and partial orders
图和偏序的枚举和代数组合
- 批准号:
105392-2002 - 财政年份:2005
- 资助金额:
$ 1.09万 - 项目类别:
Discovery Grants Program - Individual
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$ 1.09万 - 项目类别:
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图、设计、代码和群:代数组合主题
- 批准号:
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$ 1.09万 - 项目类别:
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Algebraic combinatorics of graphs and matroids
图和拟阵的代数组合
- 批准号:
105392-2013 - 财政年份:2015
- 资助金额:
$ 1.09万 - 项目类别:
Discovery Grants Program - Individual
Algebraic combinatorics of graphs and matroids
图和拟阵的代数组合
- 批准号:
105392-2013 - 财政年份:2014
- 资助金额:
$ 1.09万 - 项目类别:
Discovery Grants Program - Individual
Algebraic combinatorics of graphs and matroids
图和拟阵的代数组合
- 批准号:
105392-2013 - 财政年份:2013
- 资助金额:
$ 1.09万 - 项目类别:
Discovery Grants Program - Individual