There a lot of classes of Signal Integrity problems in IC designing. The best place to start will be to understand basic circuit models such  R, L, C and most importantly Transmission lines. Also, for problems such as Crosstalk, familiarity with a 2D or 3D field solver will be very useful. Hope this helps.

You are forewarned that signal integrity was a hot topic about 15 years ago. Crosstalk, IR drop, Ldi/dt drop were examined by researchers. Crosstalk noise and crosstalk delay were identified as the two major problems. There are books written on this subject.and you will find their titles through a simple Google Search. Perhaps you should first read a book on the topic before you finalize your research area. Good wishes.