# Robert Rhoades : The story of a strange function

In a 1997 Fields Medalist Maxim Kontsevich suggested that the function F(q) = 1 + (1-q) + (1-q)(1-q^2) + (1-q)(1-q^2)(1-q^3)+ , defined only for q a root of unity, is similar to certain functions arising from the computation of Feynman integrals in quantum field theory. In the last sixteen years this function has been connected to interval orders in decision making theory, ascent sequences and matchings in combinatorics, and Vassiliev invariants in knot theory. Don Zagier related the asymptotic properties of this function to the half-derivatives of modular forms and was led to define a notion of quantum modular form. In a trilogy of papers, my collaborators (Andrews, Bryson, Ono, Pitman, Zwegers) and I have connected this function to Ramanujans mock theta functions and the combinatorics of unimodal sequences. I will tell the story of this function and these many relationships.

**Category**: Number Theory**Duration**: 01:04:54**Date**: December 4, 2013 at 1:55 PM-
**Tags:**seminar, UNC-Duke Number Theory Seminar Seminar

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