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.
