Conference: 40th International Conference on Quantum Probability and Infinite Dimensional Analysis

该奖项将为2019年8月12日至16日在哥伦布俄亥俄州立大学校园举行的“第40届量子概率和无限维分析国际会议”提供部分资金。这次会议代表了量子概率和无限维分析协会（AQPIDA）的年度国际会议。这将是在美国举办的第一次量子概率会议。AQPIDA成立旨在促进量子概率领域的发展，这是由约翰·冯·诺伊曼发起的数学领域，几乎与安德烈·科尔莫戈洛夫创立经典概率论同时进行。经典概率论的发展非常快，但量子概率论的进展要慢得多。在过去的二十年里，量子概率论取得了巨大的进步，特别是来自意大利、日本、韩国和波兰的数学家。这次会议还将让从事经典和量子概率研究的数学家有机会聚集在一起，讨论两个领域共同感兴趣的问题，并消除分隔这两个领域的人为障碍，这将有助于刷新过去数学家和物理学家之间存在的传统合作关系。包括：编码概率测度的属性，在其量子算子方面具有所有阶的有限矩：创建、湮灭和保存算子，了解量子算子之间存在的交换关系如何导致有关相互作用系统的新物理解释，在理解量子马尔可夫链或场方面取得进展，了解量子算子之间的交换关系如何影响第二量化算子和威克乘积的内核，使用内核证明关于威克乘积范数的尖锐不等式，以及涉及第二量子化算子的超收缩不等式，在理解瞬时子与“奇异拉普拉斯”（高阶列维拉普拉斯）的联系方面取得进展，在量子马尔可夫半群及其生成元理论的发展方面取得进展，在量子网络研究方面取得进展，并在构建可靠的量子计算机方面取得进展。会议的网站如下：https://osumarion.osu.edu/events/icqp.html 该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

This award will provide partial funding for ``The 40th International Conference on Quantum Probability and Infinite Dimensional Analysis", in the period August 12-16, 2019, at The Ohio State University Campus in Columbus. This conference represents the Annual International Meeting of the Association of Quantum Probability and Infinite Dimensional Analysis (AQPIDA). It will be the first Quantum Probability Meeting organized in the United States. AQPIDA was established with the intention of promoting the area of Quantum Probability, a mathematical field started by the efforts of John von Neumann, almost simultaneously as Classic Probability was founded by Andrey Kolmogorov. The development of Classic Probability was very fast, but the progress in Quantum Probability was much slower. In the last two decades, great advancement was made in Quantum Probability, specially by mathematicians from Italy, Japan, Korea, and Poland. Our main objective, for organizing this meeting in the United States, is to promote Quantum Probability among the American mathematicians and scientists. This conference will also give the opportunity to mathematicians working in Classic and Quantum Probability to come together, discuss problems that are of common interest for both groups of people, and eliminate the artificial barriers that separate the two fields. Among the invited people, there are also several physicists, and this will contribute to the refreshing of the traditional collaboration that existed in the past among mathematicians and physicists. Strict mathematical objectives include: codifying properties of probability measures, having finite moments of all orders, in terms of their quantum operators: creation, annihilation, and preservation operators, understanding how the commutation relationships that exist among the quantum operators can lead to new physical interpretations about interacting systems, making progress in understanding the quantum Markov chains or fields, understanding how the commutation relationships among the quantum operators affect the kernels of second quantization operators and Wick products, using the kernels to prove sharp inequalities about the norms of Wick products and hypercontractivity inequalities involving the second quantization operators, making progress in understanding the connections of instantons with the ``exotic Laplacians" (higher order Levy Laplacians), making progress in the development of the theory of quantum Markov semi-groups and of their generators, making progress in the study of quantum networks, and making progress toward building a reliable quantum computer. The web-site of the conference is the following: https://osumarion.osu.edu/events/icqp.htmlThis award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.