I expose some ideas, or rather ruminations, having occurred to me during the long lockdown period. Convex geometry is an active area of mathematics. Particularly interesting is the notion of polar duality between symmetric convex sets; we have found that this notion can be applied in quantum mechanics and its cousin time frequency analysis, to analyze various uncertainty principles (Heisenberg, Donoho-Stark) and restate them in a natural geometric way, thus avoiding the pitfalls of using the traditional (co)variances which are well adapted measurements of uncertainty only for Gaussian (or almost Gaussian) distributions. Our approach will be gentle, reflecting the fact that all this is still very much work in progress.
Convex geometry, polar duality, and TFA
14.03.2022 15:00 - 16:30
Organiser:
M. Faulhuber and K. Gröchenig
Location:
SR10 (2nd floor)