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I have applied to several US grad schools for a math PhD and I wanted to know how common online interviews for international applicants are. One department that put me on their primary waitlist has told me that there are no interviews if toefl scores are adequate. My toefl ibt score of 115/120 puts me above the cutoffs for all the schools I've applied to but there are discrepancies in my record like low BSc and MA GPA and gap years which are in contrast with my high MSc GPA, GRE scores and possibly the contents of my letters of recommendation.

Do these factors increase the likelihood of an online interview and if so, would they be asking about my understanding of the basic mathematical concepts from all areas, ask me to solve difficult problems in my area of interest or be interested in checking my fluency in English and my justifications for those discrepancies? This information would help me decide how to best utilize my time in the coming few months.

I've read similar posts here about other fields but I wanted to know if things are different for a Math PhD.

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    In the US, every university is different.
    – Buffy
    Feb 22, 2023 at 11:20

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Every university has its own system. But yes, interviews are common, especially if there are questions about a candidate such as their language skills or discrepancies about their grade history.

I think it is unlikely that anyone is going to ask you specific math problems to solve in such an interview. But they may ask you about your previous classes, test your understanding of mathematical concepts (more than your ability to solve concrete problems).

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