Mathematical Sciences: Lattice Theory

这个项目是关于研究 格子 首席研究员将通过使用 艾伦·戴的一个建筑;通过使用各种各样的 格;并通过确定是否每个分配代数 格是格的同余格。 校长 研究人员还将研究生成的结构 自由格子 格是具有结构的离散数学对象 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晶格可以在许多 数学环境 这也意味着问题很容易 很难解决，而且性质很一般。 的 这项工作的结果将影响数学的许多领域， 计算机科学、社会科学和商业管理。

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.