Geometry/topology Seminar
Wednesday, January 21, 2009, 4:30pm, 119 Physics (to be confirmed)
Richard Hain (Duke)
Three-variable modular symbols for classical modular forms
Abstract:
The modular symbol of a classical modular form of weight n+2 is a homogeneous polynomial of degree n in 2 variables. Such modular symbols satisfy functional equations when the variables are acted on by SL_2(Z). These make it into a 1-cocycle on SL_2(Z). Work of Goncharov suggests that classical modular forms should also determine 3-variable modular symbols associated to GL_3(Z). The goal of this talk is to explain joint work with Aaron Pollack on finding such 3-variable modular symbols and their functional equations.

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