PI: Jinsong Wu

The analysis group has a wide range of interests, including functional analysis, harmonic analysis, (partial) differential equations, dynamical systems, and ergodic theory. We are particularly fascinated by the connections between classical analysis and the quantum world, such as quantum mechanics, quantum field theory, and quantum information. One of our group members has initiated research on Quantum Fourier analysis, which establishes a link between Fourier analysis and quantum symmetries. We anticipate discovering even deeper intrinsic connections between analysis and other fields in the future. We find that quantum Fourier analysis has applications in unitary categorification and subfactorization. There is also a theoretical connection between quantum Fourier analysis and quantum error correction, where it might aid in designing efficient error-correcting codes for mixed states in quantum information.