If you view this reply think about the topic mentioned below:
For a Digital designer to move into the analog design the first and the most interesting for research would be low size and effecient capacitors and Inductors in IC's or you can also think of reduced parasitic effects in Analog IC's. This latter is very important since for example say, you work with opamps, then your output generally get's distorted if the circuit is kept functioning for a long time. Hence think about the way to design more effecient analog circuits which you can start with the parasitic factors into consideration.