William Hornslien

Polyhedral products are certain natural subspaces of products of CW complexes constructed from the combinatorial information of a simplicial complex. They play an important role in fields such as: toric varieties, homotopy theory, algebraic combinatorics, and robotics. Motivic homotopy theory is a homotopy theory for smooth algebraic varieties. In this talk we'll introduce polyhedral products, generalize them to an oo-categorical setting and prove some general results before applying them answer some questions about a family of toric varieties in the motivic homotopy category.