What are the standard problems we can reduce from to prove $\Omega(n\log n)$ lower bounds?Of course, state problems other than sorting and element distinctness. 
Problems to reduce from to prove an $\Omega(n\log n)$ lower bound
cc.complexity theory;lower bounds
Ben-Or directly proved  $\Omega(n\log n)$ lower bounds for several fundamental problems in the algebraic computation tree model:Element distinctness: Given an array of $n$ real numbers, are its elements distinct?Set disjointness: Given two sets of $n$ real numbers, do they have an element in common?Set equality: Given two sets of $n$ real numbers, is one array a permutation of the other?Measure problem: Given $n$ real intervals, what is the total length of their union?Set inclusion: Given two sets of real numbers, is one a subset of the other?Permutation Parity: Given an permutation of the set $[n]$, is the permutation even or odd?The first three are the ones most often used in computational geometry.