Antun Milas (Albany)
Abstract
To any graph with n nodes we associate two n-fold q-series, with single and double poles, closely related to Nahm's sum associated to a positive definite symmetric bilinear form.
Quite remarkably series with "double poles" sometimes capture Schur's indices of 4d N = 2 superconformal field theories (SCFTs) and thus, under 2d/4d correspondence, they give new character formulas of certain vertex operator algebras.
If poles are simple, they arise in algebraic geometry as Hilbert-Poincare series of "graph" arc algebras. These q-series are poorly understood and seem to exhibit peculiar modular transformation behavior. In this talk, we explain how these "counting" functions arise in different areas of mathematics and physics.
This talk will be fairly accessible, assuming minimal background. No familiarity with concepts like vertex algebras and 4d N=2 SCFT is needed.