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

Ohio State University, The, Columbus OH

Investigators

Abstract

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.html This 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.