While a simplex can be defined as a power set of a finite set, it is easier to think of them as n-dimensional objects like points, line segments, triangles, tetrahedra, etc. A simplicial complex is an object built out of these simplexes, and a special class of these called pseudo-manifolds can help us model, visualize and classify unusual topological objects, particularly 2-dimensional and 3-dimensional surfaces. The talk will deal with set theory, graph theory, some linear algebra and computer programming, and should be accessible to students who have taken or are currently enrolled in Math 2101 and 2150.