What are the relationships between those hypotheses in Fine-Grained Complexity Theory? 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/complexity2015

Here are some important hypotheses:

ETH: $3$-$SAT$ requires $2^{\delta n}$ time for some $ \delta &gt; 0$.

SETH: for every $\varepsilon &gt; 0$, 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 $n^{2-o(1)}$ time
OV 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 Ryan’s 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
This is a recent paper introducing Nondeterministic Strong Exponential Time Hypothesis (NSETH), which is an extension of SETH.

NSETH: For every $\epsilon &gt;0$, there is a $k$ such that $k$-DNF-TAUT cannot be solved in nondeterministic time $2^{(1-\epsilon)n}$.

NSETH implies SETH. If NSETH is true, then some problems do not have SETH lower bounds (because they have nondeterministic algorithms faster than deterministic algorithms). 

This paper also introduced Non-uniform Nondeterministic Strong Exponential Time Hypothesis (NUNSETH), a hypothesis stronger than NSETH and SETH.

NUNSETH: For every $\epsilon &gt;0$, there is a $k$ such that $k$-DNF-TAUT cannot be recognized by nondeterministic circuit families of size $2^{(1-\epsilon)n}$.