Hi,
I understand that you never actually worked in Denmark, but have performed your work for the danish University from a computer at you home in Switzerland.
Accoring to the EU-rules regarding coordination of social security you must as a starting point be insured in the country where you physically work – in your case Switzerland.
There are some special situations/exceptions to this. These situations are where you work in two countries at the same time, are a posted worker or a cross-border worker. But none of these situations apply in your situation.
So, you should have been insured in Switzerland, not in Denmark.
It is not relevant where you have permanent address or pay tax – it is where you physically perform your work that is important in relation to find out in which EU country you must be insured against unemployment.
Best regards,
Anders Weber, A-kasser.dk