"I studied at Oxford University from 2003 to 2006." When mentioning a time period, we use the simple past.

Yes, as Topo Morto says, past simple please. It's because it IS in the past. You have a time period... in the past. Finished. Completed. I ate pizza yesterday. From 9 a.m. to 11 a.m. I studied, but after that I fell asleep! (both the studying and the sleeping are finished/I must be wake now to be writing this!) If the time period continues up to the present then the present perfect makes sense. I have studied at Oxford since 2010 (I am still there). Or the present perfect continuous: I have been studying in London since April. So if the time period extends to the present the present perfect can be used. In England we nearly always use the present perfect in these situations. In the USA they often use the past simple still. I have heard many Americans saying "Did you have breakfast yet?" whereas we would be more likely to say "Have you had breakfast yet?" My American friends can tell you more about this.