I am an undergraduate majoring in Computer Science and Mathematics. For my undergraduate research, I would like to work on something that lies in the overlap between systems research and theoretical computer science. Something that could satisfy this requirement is cache-oblivious algorithms because it is about the analysis and design of algorithms without completely ignoring how actual systems work (memory hierarchy and so on). But there could be many other fields in systems research which involve a lot of theory, or vice versa.
One of my seniors suggested distributed systems - he seemed to indicate that things like Paxos and Raft have a lot of underlying theory, but I haven't taken the time to dig into it.
You could also suggest some field in systems research which can gain a lot from some rigorous mathematical foundations and analysis. A senior will be going to graduate school at Johns Hopkins University to do a PhD on the math behind deep learning. So maybe I could try something like "the math behind --some systems research field--".
Another example I found is "Distributed Computing using Combinatorial Topology".
TL;DR: What fields/topics of research lie in the intersection of theoretical computer science and systems research?