Hello!

What I'd like to ask is, whether there is a mathematical theory of consciousness in development or any promising serious research projects in describing conscious process mathematically or physically with sufficient mathematical background

Google 'Sir Roger Penrose' (Rouse Ball professor of mathematics at Oxford University) he worked closely with Stephen Hawking (though both have clearly different stand-points on this subject) and is arguing the case of a quantum consciousness. It deals with macroscopic phenomena and the role of microtubules. As for mathematical models of consciousness...not yet, it's still hard to define philosophically let alone mathematically.