Geometry and Complexity Theory
Geometry and Complexity Theory
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几何与复杂性理论
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
J. Landsberg
中科院分区：
文献类型：
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作者：
J. Landsberg
计算机科学中的两个核心问题是p vs np和矩阵乘法的复杂性。第一个也是数学中最伟大的未解决问题的领先候选人。第二个具有巨大的实用和理论上的重要性。代数几何和代表理论为在这些问题上推进工作和其他复杂性的工作提供了肥沃的基础。这本针对计算机科学和数学研究生和研究人员的代数复杂性理论的简介，具有具体示例，这些示例证明了几何技术在现实世界中的应用。由该领域的著名专家撰写，它提供了许多开放性问题，以激发未来的研究。复杂性理论使经典的几何问题恢复活力，并以新的方式将不同的数学领域融合在一起。这本书将展示结果出现的美丽，有趣且重要的问题。
Two central problems in computer science are P vs NP and the complexity of matrix multiplication. The first is also a leading candidate for the greatest unsolved problem in mathematics. The second is of enormous practical and theoretical importance. Algebraic geometry and representation theory provide fertile ground for advancing work on these problems and others in complexity. This introduction to algebraic complexity theory for graduate students and researchers in computer science and mathematics features concrete examples that demonstrate the application of geometric techniques to real world problems. Written by a noted expert in the field, it offers numerous open questions to motivate future research. Complexity theory has rejuvenated classical geometric questions and brought different areas of mathematics together in new ways. This book will show the beautiful, interesting, and important questions that have arisen as a result.