Mathematical Sciences: Lattice Theory

本课题致力于研究晶格的结构。主要的研究人员将通过利用Alan Day的构造、通过使用各种格以及通过确定每个分配代数格是否是格的同余格来实现这一点。首席研究员还将研究有限生成的自由格的结构。格是离散的数学对象，其结构在某种程度上反映了集合论或逻辑的结构。这种非常弱的结构意味着格子可以在许多数学环境中找到。这也意味着问题很容易陈述，很难解决，而且具有非常普遍的性质。这项工作的成果将对数学、计算机科学、社会科学和企业管理的许多领域产生影响。

This project is concerned with studying the structure of lattices. The principal investigator will do this by making use of a construction due to Alan Day; by using varieties of lattices; and by determining whether every distributive algebraic lattice is the congruence lattice of a lattice. The principal investigator will also study the structure of finitely generated free lattices. Lattices are discrete mathematical objects with a structure reflecting, to some extent, the structure of set theory or logic. This very weak structure means that lattices can be found in many mathematical environments. It also means that problems are easy to state, hard to solve and of a very general nature. The results of this work will impact many areas of mathematics, computer science, the social sciences and business management.