Jie Du University of New South Wales Infinitesimal quantum gln and little q-Schur algebras Friday 11th June, 12:05-12:55pm, Carslaw 373. We first follow De Concini and Kac to give a presentation for the infinitesimal quantum gln, uk(n), and then reconstruct or realize uk(n) in two different ways following the Beilinson-Lusztig-MacPherson geometric setting approach. Thus, we obtain three new bases for uk(n). Then, we use uk(n) to introduce the little q-Schur algebra uk(n,r) as a subalgebra of the q-Schur algebra Uk(n,r). The symmetry structure of a little q-Schur algebra is then investigated through the construction of various bases of monomial, BLM and PBW types for uk(n) and q-Schur algebras. We also obtain a formula for the dimension of uk(n,r).