Representation Theory, Geometry, and Cohomology in Tensor Triangulated Categories
Representation Theory, Geometry, and Cohomology in Tensor Triangulated Categories
批准号:
1402271
负责人:
Daniel Nakano
金额:
$15.83万
依托单位国家:
美国
项目类别:
Standard Grant
财政年份:
2014
资助国家:
美国
项目状态:
已结题
起止时间:
2014-09-01 至 2018-08-31
中文摘要
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英文摘要
Algebraic structures like groups, Lie algebras, and Lie superalgebras have internal symmetries that have been used in many different physical applications in biology, chemistry, and physics. Representation theory, a method to codify information about groups and algebras through matrix realizations, has played a fundamental role in mathematics over the past one hundred years. Modern trends in representation theory have involved using tools from topology (i.e., cohomology) and algebraic geometry to package the representations of an algebraic object via the tensor product structure to connect the representation theory to ambient geometric structures. This project will use these deep interactions between the representations, the geometry, and the cohomology as a powerful device to prove new results about these algebraic structures and to answer important questions pertaining to geometric and homological invariants (like the complexity and atypicality) for these representations. The PI will organize conferences in algebra with an emphasis toward the development of junior mathematicians, and he will disseminate working knowledge of modern methods in representation theory through lectures at seminars, workshops, and summer schools.This project explores central problems of interest in the representation theory of reductive algebraic groups, Lie algebras, and Lie superalgebras. This study includes discovering new conjectures about the characters of simple modules for reductive algebraic groups in positive characteristic, and classical Lie superalgebras in characteristic zero. The determination of formulas for extensions between irreducible representations for finite Chevalley groups and loop algebras will also be explored. In this investigation, the PI will make use of tensor triangulated geometry and other geometric constructions in triangulated categories to compute cohomological invariants (e.g. cohomology groups, module varieties) of representations for the aforementioned algebraic objects.
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Representation Theory and Geometry in Monoidal Categories
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批准号:2401184
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项目类别:Continuing Grant
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资助金额:$25.53万
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财政年份:2024
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负责人:Daniel Nakano
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依托单位:
Monoidal Triangular Categories: Representation Theory, Cohomology, and Geometry
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批准号:2101941
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项目类别:Standard Grant
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资助金额:$23.24万
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财政年份:2021
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负责人:Daniel Nakano
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依托单位:
Representations, Cohomology, and Geometry in Tensor Triangulated Categories
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批准号:1701768
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项目类别:Continuing Grant
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资助金额:$16.5万
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财政年份:2017
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负责人:Daniel Nakano
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依托单位:
Cohomology, Geometry and Representation Theory: Algebraic Groups, Quantum Groups and Lie Superalgebras
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批准号:1002135
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项目类别:Standard Grant
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资助金额:$17.0万
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财政年份:2010
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负责人:Daniel Nakano
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依托单位:
Vertical Integration of Research and Education in Mathematics at the University of Georgia
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批准号:0738586
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项目类别:Continuing Grant
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资助金额:$381.99万
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财政年份:2008
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负责人:Daniel Nakano
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依托单位:
Cohomological Methods in the Representation Theory of Algebraic Groups, Quantum Groups and Superalgebras
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批准号:0654169
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项目类别:Continuing Grant
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资助金额:$15.97万
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财政年份:2007
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负责人:Daniel Nakano
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依托单位:
Cohomology and Representation Theory
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批准号:0400548
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项目类别:Standard Grant
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资助金额:$11.84万
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财政年份:2004
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负责人:Daniel Nakano
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依托单位:
Cohomology and Representation Theory: Reductive Algebraic Groups and Related Structures
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批准号:0136082
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项目类别:Standard Grant
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资助金额:$10.1万
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财政年份:2001
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负责人:Daniel Nakano
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依托单位:
Cohomology and Representation Theory: Algebraic Groups, Finite Groups and Lie Algebras
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批准号:9800960
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项目类别:Standard Grant
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资助金额:$7.29万
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财政年份:1998
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负责人:Daniel Nakano
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依托单位:
Mathematical Sciences: Cohomology and Representation Theory of Algebraic Groups and Lie Algebras
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批准号:9500715
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项目类别:Standard Grant
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资助金额:$5.91万
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财政年份:1995
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负责人:Daniel Nakano
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依托单位:
Mathematical Sciences: Postdoctoral Research Fellowship
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批准号:9206284
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项目类别:Fellowship Award
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资助金额:$7.5万
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财政年份:1992
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负责人:Daniel Nakano
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依托单位:
国内基金
海外基金
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