Well-quasi-ordering for binary matroids

在拟阵表示论中，我们研究自然的几何问题，例如：“我们什么时候可以嵌入一组点在一个空间中受到规定的依赖关系？“这些问题类似于占据古典希腊几何学家，如欧几里得和帕普斯。 虽然这些问题本质上是理论性的，但动机是回答组合优化和理论计算机科学中的基本问题。 所提出的研究的目标是提供结构性的结果有关的配置点在“有限射影几何”。研究计划目前正处于一个非常激动人心的阶段。有一个很好的机会，在不久的将来，我们将能够回答一些最古老和最基本的问题，在该地区，即罗塔猜想和良好的准序猜想。 如果成功，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领域，利用有限射影几何，如编码理论和密码学。

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.