Combinatorics of coxeter groups and relations with their relative structures

虽然我的研究项目涉及一些抽象的代数结构(Coxeter群)的研究，但它承认从理论物理到统计学的各种分支，贯穿于其他数学领域的各种应用。Coxeter群自然地表现为正多面体的一组变换(对称性)，因此在结晶学中扮演着重要的角色。它们几乎在数学的所有领域都能找到。例如，与单李代数和Kac-Moody代数有关，或者在欧几里得几何和双曲几何的某些方面的精细研究。

Although my research program concerns the study of some abstract algebraic structures (Coxeter groups), it admits ramifications ranging from theoretical physics to statistics, throughout various applications in other fields of mathematics. Coxeter groups appear naturally as a set of transformations (symmetry) of regular polyhedrons, and therefore are playing an important role in crystallography. They can also be found virtually in almost all areas of mathematics. For example in relation to simple Lie algebras and Kac-Moody algebras, or in some aspects of refined study of Euclidean geometry and hyperbolic geometry.