Xiaoping Xu Institute of Mathematics, Chinese Academy of Sciences Path hypergeometric functions and representations of gl(n) Friday 18th June, 12:05-12:55pm, Carslaw 373. Trace functions of intertwining operators among gl(n)-modules were introduced by Etingof in connection with the solutions of the Calogero-Sutherland model. We find the explicit formulae for trace functions under certain conditions. If n=2, the master function of the trace function is exactly the classical Gauss hypergeometric function. When n>2, the master functions of the trace functions are a new family of multiple hypergeometric functions, whose differential property and integral representation are determined by some polynomials associated with integral paths connecting pairs of positive integers.