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Lie Group Quantum Mathematics Seminar

Graph q-series, graph schemes, and 4d/2d correspondences

Antun Milas, SUNY-Albany

Location:  zoom
Date & time: Friday, 19 February 2021 at 12:00PM - 1:00PM

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.

Zoom link:
Meeting ID: 939 2146 5287
Passcode: 196884

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