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Explore advanced mathematical concepts in this one-hour lecture on non-perturbative deformation quantization, where the formality theorem's application to Poisson varieties and their canonical sheaf of algebroids over $\mathbb C[[\hbar]]$ is examined. Delve into a new conjecture proposing that compact manifolds of Kähler type possess a canonical global category for any $\hbar\in \mathbb C$, alongside a companion conjecture concerning global categories of "compactly supported" objects on open symplectic leaves. Learn how these theoretical frameworks contribute to the formal deformation of the category of perfect complexes.
