Visa to HK for a conference.

Foreigners who apply in South Korea have to provide their ARC (alien registration card). If you have such a card, you can apply there. You need to provide: your passport and travel documents, a hk application form affixed with passport size photo, an invitation letter in which the sponsor agrees to provide financial support and accommodation, and one copy of the sponsor's HK ID

I got this idea and I've gone through the visa procedure in the internet. But my case is a bit different. I will be attending the conference at a university in HongKong and I'll only receive the invitation letter from that university and they are not my sponsor. I'll be sponsored by my Professor who is here in Korea. Is there any different criteria for this kind?

And when I apply for it, should I send those documents to HK or is there an embassy or consulate in Korea where the visa will be processed?

Invitation letter from HK is ok, and better prepare an sponsorship letter from the said professor in Korea. You can submit your application to the embassy or consulate where hold the consular jurisdiction of the place you reside now. They will send your application to HK for approval if necessary.