Connections in between K - Theory and also PDEs?

I've lately invested time understanding (the really essentials of) K - concept for $C^*$ - algebras and also topological K - concept. In fact, my major areas of passion are PDEs and also relevant subjects, specifically useful calculus for boundless drivers, Sobolev/Bessel potential/Besov rooms, interpolation concept, semigroups and more. You understand. Currently I would love to grow (and also widen) my expertise concerning the equipment of K - concept, preferably by finding out some intriguing link to claimed PDE - relevant subjects such as as an example some PDE - pertinent outcome confessing an evidence with a k - logical flavour. Or some basic suggestion just how K - concept could give understanding right into (or an intriguing perspective on) some PDE - relevant outcomes or principles.

So I would certainly be really glad, and also I wish this demand is not also wide, if you can give me with some instances of intriguing relationships, if they exist, in between K - concept and also stated PDE - relevant subjects.