Abstract: Hochster's Formula is a valuable correspondence that allows one to calculate the Betti numbers of a squarefree monomial ideal by looking at homologies of the associated Stanley-Reisner complex. I'll review Hochster's Formula with lots of pictures and examples. I'll also talk about work with Hailong Dao in which we look at a particular Betti number and show how it relates to the combinatorics of the complex. No prior knowledge of Hochster's Formula or simplicial homology will be assumed. In particular, grad students unfamiliar with the Stanley-Reisner correspondence should be able to get a feel for this active area of combinatorial commutative algebra.
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