I'm applying for Ph.D. in Mathematics and I'm writing a statement of purpose (or SOP) where I plan to express my interest in geometric representation theory and categorification. To me, an intriguing aspect of the field is that a mature understanding of mathematical objects sometimes results in their categorification, i.e. discovery of certain categories containing strictly more abundant information than the previous objects.
I only have advanced undergraduate knowledge of mathematics and the above statement is solely based on what I tried to understand from folklore and a few examples, such as Khovanov homology, which I heard of because they are relevant to my BS degree(physics). Technically, I understand the basics of category theory but not more.
Of course, I will be as honest about my current knowledge as I can. Is it favorable to state my attention to such topics when I have neither deep nor working knowledge of them?