In this talk I revisit an idea of Vladimir Zeitlin and explore quantization theory for finite-dimensional analogs of the 2D incompressible Euler equations. The approach gives rise to spatial and temporal discretizations that preserve all underlying geometric features (in particular Casimir functions and the Lie-Poisson structure). It enables numerical experiments of the long-time behavior of 2D fluids - a long standing problem in hydrodynamics. For geometric reasons the approach works much better on the sphere than on the flat torus Zeitlin used. I shall also discuss how the quantized equations themselves may give insights to the 2D Euler dynamics, following up an idea by Shnirelman.
The talk will be via Zoom at:
https://utoronto.zoom.us/j/99576627828
Passcode: 448487