Well-quasi-ordering for binary matroids

在拟阵表示理论中，我们研究自然几何问题，例如：“我们什么时候可以在满足指定依赖关系的空间中嵌入一组点？”这些问题与欧几里德和帕普斯等希腊经典几何学家提出的问题类似。虽然这些问题本质上是理论问题，但动机是回答组合优化和理论计算机科学中的基本问题。拟议研究的目标是提供关于“有限射影几何”中点的配置的结构结果。研究计划目前正处于一个非常令人兴奋的阶段。在不久的将来，我们很有可能回答该领域中一些最古老和最基本的问题，即罗塔猜想和良准有序猜想。如果成功，这些结果将在组合优化中有算法应用，例如解决某些多商品运输问题和某些整数规划问题。这些结果也可以应用于其他利用有限射影几何的领域，如编码论和密码学。

In Matroid Representation Theory we study natural geometric questions such as: "When can we embed a set of points in a space subject to prescribed dependencies?" These are similar to the questions that occupied classical Greek geometers such as Euclid and Pappus.  While the questions are theoretical in nature, the motivation is to answer fundamental problems in Combinatorial Optimization and in Theoretical Computer Science.  The goal of the proposed research is to provide structural results concerning configurations of points in "finite projective geometries". The research program is at a very exciting phase at the moment. There is a good chance that in the near future we will be able to answer some of the oldest and most fundamental problems in the area; namely Rota's Conjecture and the Well-Quasi-Ordering Conjecture.  If successful, the results will have algorithmic applications in combinatorial optimization, solving, for example, certain multicommodity transportation problems and certain integer programming problems. The results may also find application in other areas that utilize finite projective geometries, such as coding theory and cryptograpy.