Đorđe Baralić, Constructions in toric topology and their applications

Toric topology is a growing research field on the intersection of algebraic topology, algebraic geometry, combinatorics, commutative algebra and others. In this lecture, we summarize some of the most exciting developments in this area over the last three decades, starting from the seminal paper of Davis and Januszkiewicz to the extraordinary Buchstaber and Panov monograph. We introduce the classical objects studied in toric topology, such as the polyhedral product functors and quasitoric manifolds and discuss some thrilling applications.