Francesca Ferrari, SISSA

Theory Seminar

Title: Modularity of 3-manifold invariants

Abstract:
Since the 1980s, the study of invariants of 3-dimensional manifolds has
benefited from the connections between topology, physics and number
theory. Recently, a new topological invariant has been discovered: the
homological block (also known as the half-index of certain 3d N=2
theories). When the 3-manifold is a Seifert manifold given by a
negative-definite plumbing the homological block turned out to be
related to false theta functions and characters of logarithmic VOA’s. In
this talk I describe the role of quantum modular forms, false and mock
theta functions in the study of the topology of 3-manifolds. The talk is
based on the article 1809.10148 and work in progress with Cheng, Chun,
Feigin, Gukov, and Harrison.