Theoretical Physics Seminar: Davide Passaro

Title: 3-manifolds and VOAs through Ẑ invariants

Abstract: Q-series are a concise and elegant way of encoding physical and mathematical information into a single function. Examples of such q-series are the Ẑ 3-manifold invariants also known as homological blocks. Surprisingly Ẑ invariants appear in widely different areas throughout mathematics and physics, such as low dimensional topology and vertex operator algebras (VOA). The appearance of the Ẑ invariants in these two contexts originates from the unexpected number theoretical properties that Ẑ invariants have. In this talk I will discuss how the connection between 3-manifolds and  VOAs was established and how it has led to an increased understanding of the number theoretical aspects of Ẑ invariants.