I'm looking for someone knowledgeable in the mathematics of group theory and/or topology to make me understand it well enough so I can apply it to the art of cardistry.
I know how this sounds, but bear with me. If you're not familiar with cardistry, it's simply taking a deck of cards and shuffling/flourishing it around in visually pleasant ways. The packets have defined parameters, and the fingers have limited degrees of freedom. I believe that the various fingers/hands operations on the deck/packets of cards can be mathematically described,

In my attempt to define the fundamentals of cardistry, I came up with the idea of joining mathematics with it. However, I'm not certain how to accurately define a fundamental operation on a packet of cards. However, I'm certain that a combination of topology and group theory can be used to describe such actions, and even determine as-of-yet undiscovered moves.

There is no rush for this, I'm not taking any course on it, I simply want to learn this on my spare time.
I have no idea how long it will take.