How to make my IBD experience relevant to Harvard

Making IBD relevent to grad study I think is the much easier question. You produce reams of books and analysis, develop a strong work ethic, get a good sense of professionalism and what a finished product should look like, gain significant insights into an industry (if you are in a generalist program, replace with ability to analyze and adapt to different industries) and had to constantly work with peers (i.e. through getting information from the client, delegating to/taking delegations from other bankers.

The first question is much harder - you don't learn anything wrt math in banking - all the concepts are high school level, and usually you'll have a program / macro that will simply do that math for you. In terms of analytical skills (I am assuming you mean regarding analysis and not analytics), again you simply write down what your senior tells you to. However, if you want to generic this could be easily spun to say that you assessed the merits of several strategic alternatives of a company based on XYZ (offer price, synergy possibilities, etc.), built financial models which helped determine the correct course of action, wrote CIMs / other marketing materials including company trends and deep industry analysis, etc.

Bottom line is nothing will be groundbreaking - every junior banker gets more or less the same experience and will likely try and do the above. If you put quick and specific anecdotes as opposed to skills, you will be separate the wheat from the chaff. For example, "Performed (this analysis) and recognized (a trend) that allowed our client, a strategic buyer, to acquire ABC for less than other financial buyers"