I will try to outline two problems in noncommutative geometry, both related to combi- natorics and enumerative geometry, where tools from topological recursion permitted recently some significant progress. The first problem concerns higher order freeness in free probability theory. The second problem is the exact solution, order by order in their 1/𝑁-expansion, of correlation function in scalar QFT-models on noncommutative spaces.
Keywords: Matrix models; free probability; topological recursion; quantum field theory