New directions in free probability

自由概率论起源于关于算子代数结构的问题，但已经发展成为一个与许多其他完全无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，大群表示论，数学物理学，或作为应用领域的金融相关性和无线通信。自由概率论的提议者的方法在许多这些调查中发挥了重要作用。这个建议将集中在三个新的方向在自由概率：（i）量子对称性的自由概率，（ii）自由随机演算和自由Maliavan演算，（iii）运营商价值的自由概率理论。

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.