There is a lot of similarity between mice and men, but if we would simply put the DNA sequence of mouse and human next to each other they would not look very similar as they would get "out of sync". That is, where one or the species has a big lump of additional DNA, we have to offset the other sequence to see new regions of continued similarity. Doing this is an established technique and is called alignment.
Although the our DNA is basically a sequence of four different letters, it is of course also much more. The DNA houses functional elements such as genes, disease-related mutations, physical properties and much more. We are currently developing a large open-source system for analyzing relations between such DNA data sets. This is, however, restricted to comparing different data sets from the same organism.
The task is to develop a methodology for analyzing relations between DNA data sets across organisms, e.g. comparing disease-related genes in human and mouse. The existing functionality for analyzing different data sets on the same species could be used as basis. A main challenge is to handle the "warping" that is done to align the DNA sequences of different organisms.
Students should be skilled in programming and algorithms/mathematics. No prior knowledge of biology is needed, but an interest for biology could be an advantage.