From superintegrability to quasi-exact solvability: theory and application (2019–2022)
Quantum integrable systems and exact solvable models are of central importance for understanding the correct behaviors of complex quantum problems without approximation. This project aims to develop novel mathematical techniques to resolve longstanding problems in the area of integrability and exact solvability. The project investigates a variety of models, based on recent progress of the investigators, and the expected outcomes include advancement of the entire field. Anticipated applications of the proposed research include the accurate prediction of physical phenomena, from energy spectra to quantum correlations. Such advances should have significant ramifications, and provide benefits, well beyond the mathematical discipline itself.