FRG: Collaborative Research: Matroids, Graphs, and Algebraic Geometry
FRG:协作研究:拟阵、图和代数几何
基本信息
- 批准号:2053243
- 负责人:
- 金额:$ 29.57万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2021
- 资助国家:美国
- 起止时间:2021-07-01 至 2025-06-30
- 项目状态:未结题
- 来源:
- 关键词:
项目摘要
Recent advances in matroid and graph theory fuse the methods of combinatorics with concepts from algebraic geometry to resolve longstanding conjectures and provide deep insights into widespread phenomena such as unimodality and log concavity of integer sequences. The influences between combinatorics and algebraic geometry flow fruitfully in both directions; combinatorial constructions such as graph complexes have recently led to resolutions of long-standing conjectures in the geometry of moduli spaces of curves. The PIs will join forces and forge timely new collaborations to address the most pressing open problems at the interface between matroids, graphs, and algebraic geometry. The project includes the participation of graduate students and postdocs.This focused research group will build on recent breakthroughs to accomplish the following goals: 1. Study matroidal generalizations of Kontsevich’s graph complex and pursue applications to the top weight cohomology of moduli spaces of abelian varieties; 2. Investigate K-theoretic analogs of the Chow ring of a matroid, with a view toward a matroidal analog of the Hecke algebra and applications to matroidal Kazhdan-Lusztig theory; 3. Prove a categorification of the Hodge-Riemann bilinear relations in the presence of a finite group action, and pursue equivariant log concavity for the characteristic polynomial of a matroid with automorphisms; 4. Use methods inspired by the hard Lefschetz theorem to attack both the Welsh conjecture on the number of isomorphism classes of matroids of given size and rank and the Harary edge reconstruction conjecture for graphs.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.
拟阵和图论的最新进展融合了组合数学的方法和代数几何的概念,解决了长期存在的问题,并对整数序列的单峰和对数等普遍现象提供了深刻的见解。组合学和代数几何之间的影响在两个方向上都很有成效;组合结构,如图复形,最近导致了曲线模空间几何中长期存在的问题的解决。 PI将联合起来,及时建立新的合作,以解决拟阵,图和代数几何之间的接口最紧迫的开放问题。本计画包括研究生与博士后的参与,此研究小组将以最新的研究成果为基础,达成下列目标:1。研究Kontsevich图复形的拟阵推广,并寻求其在阿贝尔簇模空间的顶权上同调中的应用; 2.研究拟阵的Chow环的K-理论类似物,着眼于Hecke代数的拟阵类似物和拟阵Kazhdan-Lusztig理论的应用; 3.证明了有限群作用下Hodge-Riemann双线性关系的一个分类,并对具有自同构的拟阵的特征多项式进行了等变对数逼近; 4.利用硬Lefschetz定理启发的方法来攻击关于给定大小和秩的拟阵的同构类的数量的Welsh猜想和图的Harary边重构猜想。该奖项反映了NSF的法定使命,并通过使用基金会的智力价值和更广泛的影响审查标准进行评估而被认为值得支持。
项目成果
期刊论文数量(2)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Equivariant Kazhdan–Lusztig theory of paving matroids
- DOI:10.5802/alco.281
- 发表时间:2022-02
- 期刊:
- 影响因子:0
- 作者:Trevor K. Karn;George D. Nasr;N. Proudfoot;Lorenzo Vecchi
- 通讯作者:Trevor K. Karn;George D. Nasr;N. Proudfoot;Lorenzo Vecchi
K-rings of wonderful varieties and matroids
奇妙品种和拟阵的 K 形环
- DOI:10.1016/j.aim.2024.109554
- 发表时间:2024
- 期刊:
- 影响因子:1.7
- 作者:Larson, Matt;Li, Shiyue;Payne, Sam;Proudfoot, Nicholas
- 通讯作者:Proudfoot, Nicholas
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Nicholas Proudfoot其他文献
What is the Dowling–Wilson conjecture?
什么是道林-威尔逊猜想?
- DOI:
- 发表时间:
- 期刊:
- 影响因子:0
- 作者:
Tom Braden;Jacob P. Matherne;Nicholas Proudfoot - 通讯作者:
Nicholas Proudfoot
On the enumeration of series-parallel matroids
关于串并联阵的枚举
- DOI:
- 发表时间:
2024 - 期刊:
- 影响因子:0
- 作者:
Nicholas Proudfoot;Yuan Xu;Benjamin Young - 通讯作者:
Benjamin Young
emK/em-rings of wonderful varieties and matroids
美妙的簇和拟阵的 emK/em 环
- DOI:
10.1016/j.aim.2024.109554 - 发表时间:
2024-04-01 - 期刊:
- 影响因子:1.500
- 作者:
Matt Larson;Shiyue Li;Sam Payne;Nicholas Proudfoot - 通讯作者:
Nicholas Proudfoot
Quantizations of conical symplectic resolutions
锥辛分辨率的量化
- DOI:
10.24033/ast.1009 - 发表时间:
2018 - 期刊:
- 影响因子:0
- 作者:
Tom Braden;Anthony Licata;Nicholas Proudfoot;Ben Webster - 通讯作者:
Ben Webster
Hyperplane arrangements and <em>K</em>-theory
- DOI:
10.1016/j.topol.2005.12.005 - 发表时间:
2006-09-01 - 期刊:
- 影响因子:
- 作者:
Nicholas Proudfoot - 通讯作者:
Nicholas Proudfoot
Nicholas Proudfoot的其他文献
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{{ truncateString('Nicholas Proudfoot', 18)}}的其他基金
Kazhdan-Lusztig Theory of Matroids
Kazhdan-Lusztig 拟阵理论
- 批准号:
1954050 - 财政年份:2020
- 资助金额:
$ 29.57万 - 项目类别:
Standard Grant
Geometry and Representation Theory of Symplectic Resolutions
辛分辨率的几何和表示论
- 批准号:
1565036 - 财政年份:2016
- 资助金额:
$ 29.57万 - 项目类别:
Standard Grant
Conference: Representation Theory and Symplectic Algebraic Geometry
会议:表示论与辛代数几何
- 批准号:
1201580 - 财政年份:2012
- 资助金额:
$ 29.57万 - 项目类别:
Standard Grant
CAREER: Geometric category O and symplectic duality
职业:几何范畴 O 和辛对偶性
- 批准号:
0950383 - 财政年份:2010
- 资助金额:
$ 29.57万 - 项目类别:
Continuing Grant
Nuclear RNA surveillance of genome expression: From yeast to mammals
基因组表达的核 RNA 监测:从酵母到哺乳动物
- 批准号:
BB/F010273/1 - 财政年份:2007
- 资助金额:
$ 29.57万 - 项目类别:
Research Grant
Topology of Symplectic Algebraic Varieties
辛代数簇的拓扑
- 批准号:
0738335 - 财政年份:2007
- 资助金额:
$ 29.57万 - 项目类别:
Standard Grant
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