Mathematics Colloquia and Seminars

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Athanasiadis and Welker have recently introduced the class of Buchsbaum* simplicial complexes, which includes the class of triangulations of compact, orientable manifolds without boundary and the class of doubly Cohen-Macaulay simplicial complexes. The Lower Bound Theorem for simplicial manifolds, which was proved by Barnette and Kalai, gives sharp lower bounds on the number of faces in a simplicial polytope (more generally manifold without boundary) as a function of its dimension and number of vertices. I will begin with an introduction to these (and other) classes of simplicial complexes and discuss how to extend the Lower Bound Theorem to these new classes. This is joint work with Jonathan Browder, Michael Goff, and Isabella Novik. This is an extra seminar in the Algebra & Discrete Math seminar series. Please note the special time.