Jie Xiao Tsinghua University Affine canonical bases and representations of tame quivers Friday 10th October, 12:05-12:55pm, Carslaw 373. According to a theorem of Green and Ringel, the generic composition subalgebra of the Hall algebra provides a realization of the positive part of quantum group. By using the explicit structure of the category of representations of a tame quiver, we are able to construct a PBW-basis of the generic composition algebra with a geometric order. The matrix between this PBW-basis and a monomial basis is triangular with 1 on diagonal, then the canonical basis can be constructed by a linear algebra technique ( from Lusztig too ). The material provided in the talk is based on a joint work of Z.Lin, G.Zhang and J.Xiao.