Background: CS undergrad applying to CS PhD programs in the USA right after graduation.
As an undergrad, I research on (and will be till applications are submitted) broadly on 3 applications of a single "Technique/Algorithm".
Reasons for the domain of choice: 2 of the 3 really interest me a lot and the third I took up because the lab is well renowned in the country and I learn a lot in the process.
While this has helped me develop good skills on a technical basis, I really haven't dived deep into a particular "problem" with a fixed domain. Which is the construct of a PhD (right?).
Question 1: Will this look bad on my profile? Will it show that I'm confused?
All 3 domains, I have good research work done. I invested additional time and made sure I am not at a superficial level for any of the domains.
I actually am not confused. There is one broad problem I have in mind which I want to solve during my PhD and that involves the whole "specialisation" aspect and deep diving into a single domain. I will be mentioning this in my SOP.
I am not able to proceed with that now as I won't be able to produce anything great by my own and it demands computational resources and proper guidance which I tried but failed to obtain.
(If the answer to question 1 is yes) Question 2: Will mentioning my plan to specialise benefit me in any way in the eyes of the admission committee?
Note: If it adds any value to the question. All 3 my letter writers will be backing me for the 3 different applications I work on. 1 letter each for 1 separate broad problem that I work on. (The 3 different problems are done at 3 different labs headed by 3 different profs).