Research in Combinatorial Group Theory

研究者将致力于进一步发展和应用他强大的梯度图几何机制，该机制是为了解决著名的伯恩赛德问题（提出于1902年）而创建的，该问题是关于足够大的偶指数周期群的。特别是，他将扩展该机制的主要归纳构造的框架，以获得更多关于定义关系为n次幂的群的结果。此外，他将研究关于自由群的子群的Hanna Neumann猜想的广义版本，以及关于平凡群表示的长期存在的Stallings问题。本研究是在组合群论中，研究由产生子和定义关系式定义的群，是群理论与低维拓扑、几何和数理逻辑的交叉。群理论是一种对称的数学理论，它与许多其他学科相互作用，例如，数学之外的物理和化学，数学内部的编码理论，数论，拓扑和几何。

The investigator will work on further development and applications of his powerful geometric machinery of graded diagrams which was created to solve the famous Burnside problem (posed in 1902) on periodic groups of sufficiently large even exponents. In particular, he will extend the framework of the main induction construction of this machinery to obtain more results on groups whose defining relators are nth powers. In addition, he will work on a generalized version of the Hanna Neumann conjecture on subgroups of free groups and long-standing Stallings' problem on presentations of the trivial group.This research is in combinatorial group theory which studies groups defined by means of generators and defining relators and is at the intersection of the theory of groups with low dimensional topology, geometry, and mathematical logic. The theory of groups is a mathematical theory of symmetry which interacts with many other disciplines, for example, physics and chemistry outside of mathematics, coding theory, number theory, topology and geometry inside mathematics.