Algebra and combinatorics

代数和组合数学

• 批准号: 299310-2009
• 负责人: Faridi, Sara
• 金额: $ 1.17万
• 依托单位: Dalhousie University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2013
• 资助国家: 加拿大
• 起止时间: 2013-01-01 至 2014-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=526118
• 关键词: Algebra; combinatorics

My research is on algebraic structures called "rings". I use graphs and other such geometric structures to find algebraic properties of rings, and conversely I am interested in how the algebra of rings can affect the geometry of the objects I use. One technique that I apply often is to associate to a certain ring a graph, that is, a set of points some of which are connected by lines, or a hypergraph, which is a higher-dimensional counterpart of a graph. Using this technique I have been able to partially classify hypergraphs that correspond to rings with desirable properties from an algebraic point of view. My goal is to conduct deeper investigations in this direction and to find stronger classification techniques. The importance of this project is that many algebraic properties that are difficult to verify for a ring may be easier to verify once they are translated into properties of hypergraphs.

我的研究方向是代数结构“环”。我使用图形和其他这样的几何结构来发现环的代数性质，反过来，我对环的代数如何影响我使用的物体的几何感兴趣。我经常使用的一种技术是把一个图和一个环联系起来，也就是一组点，其中一些点是由线连接的，或者一个超图，它是一个图的高维对应物。使用这种技术，我已经能够从代数的角度对具有理想性质的环对应的超图进行部分分类。我的目标是在这个方向上进行更深入的研究，并找到更强大的分类技术。这个项目的重要性在于，许多难以验证环的代数性质一旦转化为超图的性质，就会更容易验证。