Geometric methods in group theory and group-based cryptography

群论和群密码学中的几何方法

• 批准号: 298965-2011
• 负责人: Bumagin, Inna
• 金额: $ 0.8万
• 依托单位: Carleton University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2012
• 资助国家: 加拿大
• 起止时间: 2012-01-01 至 2013-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=508433
• 关键词: Geometric; methods; group; theory; based

My research is in Pure Mathematics, more precisely, in Geometric Group Theory. This flourishing and rapidly developing field of study attracts many brilliant researchers. It is interdisciplinary in nature. It is rooted in the work of many mathematicians. It started getting its shape in the 1980s when Gromov clearly articulated the idea that infinite groups, usually regarded as algebraic objects, can be characterized by their geometric properties, and that tools from topology can be used in group theory. Since then, research in this area made its way also to harmonic analysis, logic, probability and computer science. A wealth of available techniques and potential applications ensures that the field will remain a mainstream in mathematics for a long while.

我的研究领域是纯数学，更准确地说，是几何群论。这个蓬勃发展且快速发展的研究领域吸引了许多杰出的研究人员。它本质上是跨学科的。它植根于许多数学家的工作。它在 20 世纪 80 年代开始成形，当时格罗莫夫清楚地阐明了这样的想法：无限群（通常被视为代数对象）可以通过其几何属性来表征，并且拓扑工具可以在群论中使用。从那时起，该领域的研究也扩展到调和分析、逻辑、概率和计算机科学。丰富的可用技术和潜在应用确保该领域将在很长一段时间内保持数学主流。