I'm an international student studying math and physics in an American university relatively highly ranked in terms of math. I'm currently a junior, and I'm going to focus on doing research on a certain theoretical physics topic from this summer. I've exhausted advanced grad courses offered in my university, and I don't think taking any more courses will enhance my chance in admission for math PhD programs in the U.S. Since my school doesn't have a professor working on the topic of my interest, I'm considering to work for the next year on research under the guidance of a professor, who is internationally renowned for his work in the topic, in my native country.
My concern is that there is a rumor that admission is more difficult for already graduated students. Does this thing, if true, apply to me? I'm sure master's students are demanded more, but how about me? Even though I will be in undergrad for three years only, I'm afraid they may consider me as someone who has a year of "advantage." On the other hand, I'm sure graduating a semester early doesn't affect a lot, as stated by Paul Garrett in a similar post. Could I assume Paul Garrett's comment apply to me as well? If there is an adverse effect, I can just be a student in name only for another semester or two and meanwhile do a research in my country.