Q-Series and Modularity @DIASDublin

Uploaded July 2026 | Updated September 2026, 2 weeks ago

Speaker Werner Nahm (DIAS)
Abstract: Special q-series turn up in several areas of mathematics and
mathematical physics, in particular as knot polynomials in Chern-Simons theory and as partition functions in conformal field theory. The terms of the series are fractions with a power of q in the numerator and Pochhammer symbols in the denominator. The modular (or quantum modular) nature of these series becomes manifest in their behavior near roots of unity. The latter can be studied by Lefshetz thimbles. In contrast to the usual situation, these thimbles intersect, which leads to intricate combinatorics.

$Q-Series and Modularity Speaker Werner Nahm (DIAS) Abstract: Special q-series turn up in several areas of mathematics and mathematical physics, in particular as knot polynomials in Chern-Simons theory and as partition functions in conformal field theory. The terms of the series are fractions with a power of q in the numerator and Pochhammer symbols in the denominator. The modular (or quantum modular) nature of these series becomes manifest in their behavior near roots of unity. The latter can be studied by Lefshetz thimbles. In contrast to the usual situation, these thimbles intersect, which leads to intricate combinatorics.$

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