Mathematics Colloquia and Seminars

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Diagrams of spaces provide a convenient language for studying a collection of topological spaces that share some common algebraic or combinatorial structure. Homotopy colimits provide a means for accessing those spaces that support a natural homotopy theory. I will give a brief introduction to homotopy colimits of diagrams of spaces, including some motivating examples from different areas of math, and then focus on some applications to toric varieties. Specifically, I will show how to construct a representation of the topological space underlying a given toric variety. If time permits, I will also show how the resolution of singularities and/or the cohomology of a toric variety fit into this framework.