Math Graduate Student Seminar

$\hat Z_b$, known as the homological block or WRT block, is an invariant of 3-manifolds first introduced in the works of Gukov, Pei, Putrov and Vafa based on physics. While a full-fledged definition of $\hat Z_b$ is yet to be discovered, physics predicts that these homological blocks provide a way to categorify WRT invariants, thereby generalizing Khovanov homology. In this talk I will first review how to compute $\hat Z_b$ for some classes of 3-manifolds, and then move on to discuss some recent progress revealing interesting properties of $\hat Z_b$.