Algebra, combinatorics, and mathematical computer science

代数、组合学和数学计算机科学

• 批准号: 1000230635-2014
• 负责人: Thomas, Arthur
• 金额: $ 14.57万
• 依托单位: Université du Québec à Montréal
• 依托单位国家: 加拿大
• 项目类别: Canada Research Chairs
• 财政年份: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=695613
• 关键词: Algebra; combinatorics; mathematical; computer; science

There are many important objects in algebraic geometry and representation theory ("triangulated categories") whose structure is typically very complicated, and which are therefore difficult to study directly. I plan to study them by drawing connections to better-understood topics, such as symmetry (in more technical language, "root systems" and "Weyl groups"). Conversely, I also hope that some phenomena arising in the simple ("combinatorial") settings, may be explained by interpreting them in terms of triangulated categories. The possible connections between these two areas of mathematics have so far received insufficient attention, so now is an ideal time to pursue this research program.

在代数几何和表示理论中有许多重要的对象（“三角范畴”），它们的结构通常非常复杂，因此很难直接研究。我计划通过与更容易理解的主题建立联系来研究它们，比如对称（用更专业的语言来说，是“根系”和“Weyl群”）。相反，我也希望在简单（“组合”）设置中出现的一些现象，可以通过三角分类来解释它们。到目前为止，这两个数学领域之间可能的联系还没有得到足够的重视，所以现在是进行这项研究计划的理想时机。