Value of having done applied math research when applying to PhD programs in pure math

Question

I will be a second year math under-grad in September, and currently doing an internship at applied math research institute. Most probably, I will come up with a research paper at the end of the internship.

However, my interest after my bachelors is to do PhD in pure math from a top math school.My question is this:

Would the admission committee consider my current research since it is in applied math?

In addition, if anyone can suggest me some ideas on how can I bridge the gap between my paper in applied math and my interest in analysis, I would be extremely grateful.

P.S.: Here is a related but different question also of mine.

Answer 1

Would the admission committee consider my current research since it is in applied math?

Certainly. In my experience, nobody cares at all whether an applicant's research experience is directly related to their proposed specialty in graduate school. There are several points to keep in mind:

1. There are only a limited number of research opportunities available for undergraduates, so finding one on your very favorite topic may not be possible. Nobody would hold this against you.

2. Some topics just aren't accessible to undergraduates in the first place (e.g., motivic cohomology).

3. Most applicants don't really know what they will write their dissertations on, even if they think they do. Many will change their minds a year or two into grad school.

4. Undergraduate research in mathematics is generally not as deep as grad student research, and the specific things you learn are not crucial. Instead, the point is to see whether you have an aptitude for research and whether you enjoy it. For those purposes, the precise topic doesn't really matter. (Unless, of course, there's only one thing in the world that you would like to study, but I would consider that sort of narrowness to be a problem itself.)