Papers on pure mathematics ; Gradient and oscillation estimates and their applications in geometric PDE ; On canonical and explicit classification of algebraic threefolds ; Canonical pseudonorms on pluricanonical spaces ; The enigmatic Tate-Shafarevich group ; Eta invariants for even dimensional manifolds ; Ricci flow on 4-manifolds and Seiberg-Witten equations ; Vector bundles and adic Galois representations ; Geometry of nilpotent orbits: Results and conjectures ; Integrable connections and Galois representations ; Asymptotic Chow polystability in Kahler geometry ; Representations of metaplectic groups ; Notes on partial conjugation ; Geometric modular forms and the cohomology of torsion automorphic sheaves ; SYZ transformations for toric varieties ; Some variational problems in conformal geometry ; Geometry of tamed almost complex structures on 4-dimensional manifolds ; The arithmetic of noncongruence modular forms ; Analytic continuations of quantum cohomology ; Mathematical aspects of string duality ; The tame kernels of number fields ; Notes on MVW-extensions ; Vertex operator representations for a class of C_v graded Lie algebras ; Notes on orbifold Gromov-Witten theory ; Cohomologies and elliptic operators on symplectic manifolds ; Quasilocal mass from a mathematical perspective ; On dimension data, local vs global conjugacy ; Variational problems of Monge-Amp�ere type ; Wellposedness of the two and three dimensional full water wave problem ; Recent developments in differentiable sphere theorems ; New invariants for complex manifolds, singularities, and CR manifolds with applications ; Gross-Zagier formula and arithmetic fundamental lemma ; Integrality properties of mirror maps ; Ohsawa-Takegoshi ^2 extension theorem: Revisited