New directions in free probability

自由概率理论起源于关于算子代数结构的问题，但已经演变成一个与许多其他完全不相关的领域有联系的领域：最著名的是随机矩阵，但也有组合学、大群的表示理论、数学物理，或者作为金融相关性和无线通信等应用领域。这位提出者对自由概率理论的研究方法在许多这些研究中发挥了重要作用。这项建议将集中在自由概率中的三个新方向：(I)自由概率中的量子对称性，(Ii)自由随机微积分和自由Maliavan微积分，以及(Iii)算子值自由概率理论。

Free probability theory originated from questions about the structure of algebras of operators, but has evolved into a field with links to many other quite unrelated fields: most notably random matrices, but also combinatorics, representation theory of large groups, mathematical physics, or as applied fields as financial correlations and wireless communications. The proposer's approach to free probability theory has played a major role in many of those investigations. This proposal will concentrate on three new directions in free probability: (i) Quantum Symmetries in Free Probability, (ii) Free stochastic calculus and free Maliavan Calculus, and (iii) Operator-valued free probability theory.