What would be some implications of $NL$$=P$? Would it be possible to get recommendations on good sources/papers I can read to learn more about this? Thank you
$NL = P$ means that every language in $P$ can be decided by a nondeterministic Turing machine using at most $O(\log n)$ space, where $n$ is the size of the input.
Savitch's theorem states for all $f(n) \in \Omega(\log n)$: $NSPACE(f(n))\subseteq SPACE(f(n)^2)$.
Therefore $NL = P$ implies that every language in $P$ can be decided by a deterministic Turing machine using at most $O((\log n)^2)$ space.