Recent Advances in Hodge Theory

Preface Matt Kerr and Gregory Pearlstein; Introduction Matt Kerr and Gregory Pearlstein; List of conference participants; Part I. Hodge Theory at the Boundary: Part I(A). Period Domains and Their Compactifications: Classical period domains R. Laza and Z. Zhang; The singularities of the invariant metric on the Jacobi line bundle J. Burgos Gil, J. Kramer and U. Kuhn; Symmetries of graded polarized mixed Hodge structures A. Kaplan; Part I(B). Period Maps and Algebraic Geometry: Deformation theory and limiting mixed Hodge structures M. Green and P. Griffiths; Studies of closed/open mirror symmetry for quintic threefolds through log mixed Hodge theory S. Usui; The 14th case VHS via K3 fibrations A. Clingher, C. Doran, A. Harder, A. Novoseltsev and A. Thompson; Part II. Algebraic Cycles and Normal Functions: A simple construction of regulator indecomposable higher Chow cycles in elliptic surfaces M. Asakura; A relative version of the Beilinson-Hodge conjecture R. de Jeu, J. D. Lewis and D. Patel; Normal functions and spread of zero locus M. Saito; Fields of definition of Hodge loci M. Saito and C. Schnell; Tate twists of Hodge structures arising from abelian varieties S. Abdulali; Some surfaces of general type for which Bloch's conjecture holds C. Pedrini and C. Weibel; Part III. The Arithmetic of Periods: Part III(A). Motives, Galois Representations, and Automorphic Forms: An introduction to the Langlands correspondence W. Goldring; Generalized Kuga-Satake theory and rigid local systems I - the middle convolution S. Patrikis; On the fundamental periods of a motive H. Yoshida; Part III(B). Modular Forms and Iterated Integrals: Geometric Hodge structures with prescribed Hodge numbers D. Arapura; The Hodge-de Rham theory of modular groups R. Hain.