Research topics involving statistics and basic topology or discrete math

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I'm starting to get involve into statistic and probability topics, and would like to know if you could recommmend me a research topic about both statistics and another field such as basic topology, discrete math or another math field that doesn't require a full and deep math knowledge. Sorry if the question is too open, what I need is basically some research topics just to get a starting point in statistics research. Thank you in advance

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I recommend checking out the site Open Problem Garden (Link: http://www.openproblemgarden.org/). They have a collection of unsolved problems in mathematics. Even if none of the particular problems interest you, I'm sure you will be able to find an area that interests you.