Bijective Combinatorics of Young Tableaux

在过去的几年里，有越来越多的连接之间的枚举代数几何，特别是格罗莫夫-威滕理论，和代数组合，特别是杨tableaux身份。 提出者打算继续研究与这些恒等式有关的组合双射。特别是，他打算调查多加权类似物的某些经典组合身份也自然产生的代表性理论的对称群。他还打算追求枚举，代数和概率应用的离散随机过程产生的加权杨tableaux.Young tableaux是基本的组合结构，介绍了一百多年前与研究一大类空间的对称性。多年来，杨tableaux已进一步研究与其他领域的研究，如统计物理，离散概率，最近，代数几何和场论。 评论家打算追求后者连接的组合方面，开发新的工具，这反过来又会导致在这两个领域的新成果的意图。

In the past few years there has been a growing number of connections between enumerative algebraic geometry, in particularly Gromov-Witten theory, and the algebraic combinatorics, in particular Young tableaux identities. The proposer intend to pursue the study of combinatorial bijections related to these identities. In particular, he intends to investigate multi-weighted analogues of certain classical combinatorial identities which also arise naturally from the representation theory of the symmetric group. He also intends to pursue both enumerative, algebraic and probabilistic applications of the discrete random processes for generation of weighted Young tableaux.Young tableaux are basic combinatorial structure which were introduced over a hundred years ago in connection with studies of a large class of spaces with symmetries. Over the years, Young tableaux have been further studied in connection with other fields of studies, such as statistical physics, discrete probability, and more recently, algebraic geometry and field theory. The reviewer intends to pursue the combinatorial aspects of the latter connections, with the intension of developing new tools, which in turn will lead to new results in both fields.