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UID:node-3058843@mathematics.huji.ac.il
DTSTAMP:20211021T130000Z
DTSTART:20211021T130000Z
DTEND:20211021T141500Z
SUMMARY:Basic Notions: Ruth Lawrence (HUJI) The Quantum Modularity Conjecture - 2nd talk
DESCRIPTION:Abstract:\nOver the last 20 years, many examples have arisen, mainly from quantum \ninvariants of knots and 3-manifolds, of "expressions" in a variable q which \nare well-defined both at all roots of unity and as formal (divergent) power \nseries or asymptotic expansions around q=1 (or more generally any root of \nunity). The simplest example of such an expression is $ \sum_{n=0}^\infty \n(1-q)\ldots(1-q^n)$ (studied in Zagier [Topology 40 (2001) 945-960]) which is \non the one hand related to the combinatorics of Vassiliev invariants and on \nthe other to the Dedekind eta-function. Another early example (Lawrence & \nZagier [Asian J. Math 3 (1999) 93-108]) is the values of the quantum sl_2 \ninvariant (the Witten-Reshekhin-Turaev invariant) of the Poincare homology \nsphere, which is defined at roots of unity, and by its connection with \nWitten-Chern-Simons theory has a perturbative expansion also around q=1. In \nboth cases, connections were shown with "almost modular forms", meaning that \nthese are not modular form...
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