Complexity theory, through such concepts as NP-completeness, distinguishes between computational problems that have relatively efficient solutions and those that are intractable. Fine-grained complexity aims to refine this qualitative distinction into a quantitative guide as to the exact time required to solve problems. More details can be found here: http://simons.berkeley.edu/programs/complexity2015Here are some important hypotheses:ETH: $3$-$SAT$ requires $2^{\delta n}$ time for some $ \delta > 0$.SETH: for every $\varepsilon > 0$, there is a $k$ such that $k$-$SAT$ on $n$ variables, $m$ clauses cannot be solved in $2^{(1-\varepsilon)n}~poly~m$ time.It is known that SETH is stronger than ETH and they both are stronger than $P \neq NP$,and both stronger than $FTP\neq W[1]$. Four other important conjectures: 3SUM Conjecture: 3SUM on $n$ integers in $\{-n^3,,n^3\}$ requires $n^{2-o(1)}$ timeOV Conjecture: Orthogonal vectors on $n$ vectors requires $n^{2-o(1)}$ time.APSP Conjecture: All Pairs Shortest Path on $n$ nodes and $O(\log n)$ bit weights requires $n^{3-o(1)}$ time.BMM Conjecture: Any combinatorial algorithm for Boolean matrix multiplication requires $n^{3-o(1)}$ time.It is known that SETH implies the OV Conjecture (Ryan Willams, 2004). Besides Ryans proof that SETH $\implies$ OV Conjecture, there are no other reductions relating the conjectures known.My question: Do you know other related hypotheses or conjectures in this area? What are the relationships between them?  Acknowledgement: results listed are from the slides of  Virginia Vassilevska Williams, she also gave me partial answers to this question. Link to slides: http://theory.stanford.edu/~virgi/overview.pdf
What are the relationships between those hypotheses in Fine-Grained Complexity Theory?
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