Room 225 TMCB
Title: Cellular A^1-Homology of Smooth Toric Varieties
Abstract: In this talk, we explore the calculations of cellular A^1-homology for smooth toric varieties, an analog of classic cellular homology. We provide an explicit description of pure shellable cases and discuss the derivation of the (Milnor-Witt) motivic decomposition for these cases, inspired by classic results in real toric manifolds. These findings offer new and refined algebraic invariants for toric varieties, reflecting both their complex and real points. Additionally, we present several applications of this computation, including an ongoing work on the wonderful model of hyperplane arrangements. This is a joint work with Keyao Peng.