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

该奖项将为2019年8月12日至16日在哥伦布的俄亥俄州立大学校园举行的“第40届量子概率与无限维分析国际会议”提供部分资金。本次会议代表了量子概率与无限维分析协会（AQPIDA）的年度国际会议。这将是第一次在美国组织的量子概率会议。AQPIDA成立的目的是促进量子概率论领域的发展，量子概率论是由约翰·冯·诺伊曼（John von Neumann）的努力开创的一个数学领域，几乎与安德烈·科尔莫戈罗夫（Andrey Kolmogorov）创立经典概率论同时成立。经典概率论的发展非常迅速，而量子概率论的发展则要慢得多。近二十年来，特别是意大利、日本、韩国和波兰的数学家在量子概率论方面取得了很大的进展。我们在美国组织这次会议的主要目的是在美国数学家和科学家中推广量子概率论。这次会议还将为经典概率和量子概率领域的数学家提供机会，让他们聚在一起，讨论两组人共同感兴趣的问题，并消除将这两个领域分开的人为障碍。在受邀的人中，也有几位物理学家，这将有助于刷新过去存在于数学家和物理学家之间的传统合作。严格的数学目标包括：编纂概率测度的性质，具有所有阶的有限矩，根据它们的量子算子；创造、湮灭和保持算符，理解量子算符之间的对易关系如何导致对相互作用系统的新的物理解释，在理解量子马尔可夫链或场方面取得进展，理解量子算符之间的对易关系如何影响第二量子化算符和Wick积的核，利用核证明了关于Wick积规范的尖锐不等式和涉及第二量子化算子的超收缩不等式，在理解瞬子与“奇异拉普拉斯量”（高阶Levy拉普拉斯量）的联系方面取得了进展，在发展量子马尔可夫半群及其产生子的理论方面取得了进展，在量子网络的研究方面取得了进展。并在建造可靠的量子计算机方面取得进展。会议的网址如下：https://osumarion.osu.edu/events/icqp.htmlThis该奖项反映了美国国家科学基金会的法定使命，并通过基金会的知识价值和更广泛的影响审查标准进行评估，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.