Quantization via linear algebra and (almost) toric geometry

Quantization is notoriously difficult and even when we have found quantizations of, say, coordinate rings of varieties, these often appear ad-hoc.  But, using ideas that were just emerging when the speaker was embarking on their research journey in the Institute some twenty years ago, a remarkable alternative approach has been developed. We will describe the journey, culminating in a recent result with Pressland showing that quantization and categorification are intimately linked. Braidings, grading and mirror symmetry also feature in our story.