A celebrated problem posed by Yau is how to classify (complete) 3-manifolds with (uniformly) positive scalar curvature. It has been resolved by G.Perelman for the closed case. In this talk, we use minimal surface theory, instead of Ricci flow, to characterize the topological structure of open 3-man...

Let U be the quantum group associated to a Kac-Moody algebra of symmetric type, and U_1 the quantum group obtained from an admissible diagram automorphism s on U. Let U^-, U_1^- be the negative part of U, U_1, respectively. Lusztig constructed the canonical basis B of U^- , and the canonical signed ...