

Recent preprints: Generalization of Lawson and Simons' result to quaternion and octonion geometry, S.C. Lau and N.C. Leung Moduli of Bundles over Rational Surfaces and Elliptic Curves I: Simply Laced cases, N.C. Leung and J.J. Zhang. Moduli of Bundles over Rational Surfaces and Elliptic Curves II: Nonsimply Laced cases, N.C. Leung and J.J. Zhang. A quadratic inequality for sum of coadjoint orbits, N.C. Leung and X.W. Wang. Hard Lefschetz actions in Riemannian geometry with special holonomy, N.C. Leung and C.Z. Li. Intersection theory of coassociative submanifolds in G_2 manifolds and SeibergWitten invariants, (revised version) N.C. Leung and X.W. Wang. Mirror symmetry of FourierMukai transformation for elliptic CalabiYau manifolds, N.C. Leung and S.T. Yau, Proceedings of the Geometry Conference in Honour of Nigel Hitchin, Oxford University Press (2007). Instantons and brances on manifolds with vector cross products, J.H. Lee and N.C. Leung, to appear in Asian Journal of Mathematics. MiyaokaYau type inequalities for KahlerEinstein manifolds, K.W. Chan and N.C. Leung, Comm. Analy. Geom., vol. 15, no. 2 (2007) 359379. Higher dimensional knot spaces for manifolds with vector cross product, J.H. Lee and N.C. Leung, Advances in Mathematics, 213 (2007) 140164. HyperLagrangian submanifolds of Hyperkahler manifolds and Mean Curvature Flow, N.C. Leung and T. Wan, Journal of Geometric Analysis, vol. 17, no. 2 (2007) 343364. Counting elliptic curves in K3 surfaces, J.H. Lee and N.C. Leung, Journal of Algebraic Geometry 15 (2006), no. 4, 591601. YauZaslow formula on K3 surfaces for nonprimtive classes, J.H. Lee and N.C. Leung, Geometry and Topology 9 (2005), 19772012. Mirror symmetry without corrections, N.C. Leung, Comm. Anal. Geom. 13 (2005), no.2, 287331. Papers in Preparation: A uniform description of Riemannian symmetric spaces as Grassmannians using magic square, Y.D. Huang and N.C. Leung. Hodge theory for G_2 manifolds: Intermediate Jacobians and AbelJacobi maps, S. Karigiannis and N.C. Leung. Title TBA, N.C. Leung and Tom Wan. 