You’ve found my landing page for algorithmic information theory (AIT).

At its core, algorithmic information theory seeks to formalize notions of randomness, information content, and even logical reasoning capabilities.

And, most fruitfully, AIT has been applied to geometric measure theory (GMT): refining classic results about fractal dimension and measure via counting and computability arguments.

You can find my digitized notes on AIT by following the link below:

Algorithmic Information Theory, Notes.

Or, below is a primer document to AIT and its potential application to GMT:

AIT Primer Page

I made this video as a more basic introduction to this connection as well.