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A main area of research in combinatorial commutative algebra is to study minimal free resolutions of monomial ideals. There is a one-to-one correspondence between simplicial complexes and squarefree monomial ideals in the polynomial ring $S=k[x_1, \dots , x_n]$ by identifying the vertices with the variables in $S$ and the facets with the monomial generators. In this talk, I will discuss some results regarding connections between simplicial complexes and invariants of minimal free resolutions of associated ideals.