Mathematical Sciences: Algebraic Combinatorics

该奖项资助Sergey Fomin教授对组合学和代数之间新关系的探索。基于Yang-Baxter方程的指数解的Schubert和Grothendieck多项式理论的新方法提出了Coxeter群组合学的新发展。本工作将通过对称函数、局部结合代数和泛代数建立在此基础上。这项研究属于组合学的广泛范畴，这是当今数学中最活跃的领域之一。从根本上说，组合学是对系统计数的研究。当对象难以列出时，计数可能会非常困难，组合学家会寻找克服这些困难的通用方法。今天的组合学利用了各种最先进和现代的数学技术。虽然它的根源可以追溯到几个世纪以前，但在过去的几十年里，这个领域有了爆炸性的发展。这种增长来自于它在通信和信息技术中的重要性，以及现代技术在计数问题上的成功。＊＊＊

Fomin This award funds Professor Sergey Fomin's exploration of new relations between combinatorics and algebra. A new approach to the theory of Schubert and Grothendieck polynomials based on exponential solutions to the Yang-Baxter equations has suggested new developments in the combinatorics of Coxeter groups. This work will build on this via symmetric functions, local associative algebras and universal algebra. This research falls in the broad category of combinatorics, which is one of the most active fields in today's mathematics. At its roots, combinatorics is the study of systematic counting. Counting can be incredibly difficult when the objects are difficult to list, and combinatorists look for general methods for overcoming these difficulties. Today's combinatorics makes use of a wide variety of the most advanced and modern mathematical techniques. Although its roots go back several centuries, the field has had an explosive development in the past few decades. This growth comes from its importance in communications and information technology and from the success of modern techniques to problems of counting. ***