Well, Precomputer Radiance Transfer uses Spherical Harmonics in order to compress the reaction of each vertex with respect to each direction of light. Is there any research about how can this [lossy] compression, which could also be interpreted as a loosy construction mechanism, can be used in AI... Maybe you shouldn't strict your answer to just Spherical Harmonic... Any analogue may be ok... JUST A THOUGHT

There's not much info in your post, but it seems like you're comparing SH to other statistical data modeling methods in AI such as neural networks. Yes, if the function you're trying to represent has a sphere as its domain (or can be projected onto a sphere and still provide usable results) then SH can be useful. It has trouble representing high-frequency features, but then ANNs do too, to some extent. Keep in mind, though, that statistical data modeling is only a small area of AI, and one which is not especially useful for games (where models can usually be directly specified rather than learned from training data).

So anyway, what course or subject in colleges has to deal with these Spherical Harmonics. Am actually interested in its concept and all.

Hmm... Not sure. Signal processing classes will cover fourier and even wavelet transforms, but SH transforms are a bit esoteric, and while they have the same basic idea as other transforms, their domain makes them less useful in the field of DSP. You may need to pick it up on your own. It's as good a time as any to start tackling academic journal articles, if you don't do that already.

They crop up a lot in applied maths... I seem to recall learning about them in fluid dynamics classes... but that was more than a decade ago, so my memory is a bit rusty.

They are extremely important in quantum mechanics.