International Workshop on Operator Theory and Its Applications

该基金将为20名美国算子理论、电气工程和物理学领域的年轻科学家提供旅行支持，参加算子理论与应用国际研讨会（IWOTA），该研讨会将于2021年8月9日至13日在加利福尼亚州奥兰治的查普曼大学举行。一个重要的目标是年轻数学家的积极参与，如研究生、博士后和其他初级职位。这一目标将通过鼓励每位初级参与者发表有贡献的演讲，并为非正式讨论提供空间和未来合作的途径来实现。所有受邀的演讲者都将被要求确保他们的部分演讲能够被年轻的研究人员所理解。由于其每年的国际存在，IWOTA促进了世界各地数学网络的扩大。算符理论是分析、量子力学、理论物理、概率论、随机过程、信号处理、机器学习等多个领域的交叉点。由于量子物理可以通过应用算符理论来描述，关于量子物理和超振荡的两个特别会议处于21世纪最大挑战之一的前沿：量子计算。随机过程理论与算子理论有许多交集，这需要算子理论的深度工具来探索。随机过程及其导数（通常是广义随机过程）可以用Gelfand三元组理论来研究，Gelfand三元组理论是通过将Bochner-Minlos定理应用于Frechet核空间上的正定函数而得到的。用自由的Fock空间代替Fock空间，就得到了非交换集。同样地，用格拉斯曼代数或三元代数来代替复数，我们就得到了与超级数学和流形的新联系。其中四场特别会议聚焦于这一思想圈。最近在双复、三元和四元数分析中的研究使用算子理论技术将内在分析结构和出现的许多类型的算子联系起来，并在每种情况下获得实现公式。一些技术在更一般的超复杂环境中的适用性为物理和数字信号处理提供了更多的应用。三元代数被认为是量子场论中三夸克/反夸克可观测性问题的代数约束模型的一个有希望的候选者。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

The funds will provide travel support for up to twenty junior US based scientists in operator theory, electrical engineering and physics to attend the International Workshop on Operator Theory and Applications (IWOTA), which will be held at Chapman University, Orange, CA during August 9 - 13, 2021. An important goal is the active participation of young mathematicians, such as graduate students, post-docs, and other junior level positions. This goal will be achieved by encouraging every junior participant to give a contributed talk and by providing space for informal discussions and avenues for future collaborations. All invited speakers will be asked to ensure that part of their talks be accessible to young researchers. Due to its yearly international presence, IWOTA facilitates the enlargement of mathematics networks from all around the world.Operator Theory lies at the intersection of several fields such as analysis, quantum mechanics, theoretical physics, probability, stochastic processes, signal processing, machine learning, and many others. As quantum physics can be described via applied operator theory the two special sessions on quantum physics and on super-oscillations are at the forefront of one of the biggest challenges of the 21st century: quantum computing. The theory of stochastic processes and operator theory have numerous intersections, which require deep tools of operator theory to explore. Stochastic processes and their derivatives (usually generalized stochastic processes) may be studied using the theory of Gelfand triples, obtained by applying the Bochner-Minlos theorem to a positive definite function on a Frechet nuclear space. Replacing the Fock space by the free Fock space, one arrives at the non-commutative setting. In a similar vein, replacing the complex numbers by the Grassmann algebra or by a ternary algebra one gets new connections with super mathematics and manifolds. Four of the special sessions focus on this circle of ideas. Recent research in bicomplex, ternary, and quaternionic analysis use operator theory techniques to relate the intrinsic analytic structure and the many types of operators that arise and obtain realization formulas in each case. Applicability of some techniques in a more general hypercomplex setting provides even more applications to physics and digital signal processing. Ternary algebras are known to be a promising candidate for the algebraic confinement model for the problem of observability of three quarks/anti-quarks in Quantum Field Theory.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.