My research area is Commutative Algebra. I analyze algebraic invariants using combinatorial tools. A simplicial complex is an important combinatorial tool for studying properties of squarefree monomial ideals. In the work with my collaborators, we characterize some algebraic properties of an ideal in terms simplicial complexes associated with the ideal. Some themes include the Lefschetz properties of Artinian algebras, linear resolution and Castelnuovo-Mumford regularity of squarefree monomial ideals, vertex decomposability of simplicial complex.