PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Karl Schwede, Robert Vaughan, Mihran Papikian, Ae Ja Yee.

Title:The story of a "strange" function
Seminar:Algebra and Number Theory Seminar
Speaker:Rob Rhoades, Stanford
Abstract:
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 Ramanujan's mock theta functions and the combinatorics of unimodal sequences. I will tell the story of this function and these many relationships.

Room Reservation Information

Room Number:MB106
Date:12 / 12 / 2013
Time:11:15am - 12:05pm