# Recent Advances in Hodge Theory (London Mathematical Society Lecture Note Series)

Cambridge University Press, 2/4/2016

EAN 9781107546295, ISBN10: 110754629X

Paperback, 532 pages, 22.8 x 15.2 x 2.8 cm

Language: English

In its simplest form, Hodge theory is the study of periods Ã¢â‚¬â€œ integrals of algebraic differential forms which arise in the study of complex geometry and moduli, number theory and physics. Organized around the basic concepts of variations of Hodge structure and period maps, this volume draws together new developments in deformation theory, mirror symmetry, Galois representations, iterated integrals, algebraic cycles and the Hodge conjecture. Its mixture of high-quality expository and research articles make it a useful resource for graduate students and seasoned researchers alike.

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 BeilinsonÃ¢â‚¬â€œHodge 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 KugaÃ¢â‚¬â€œSatake theory and rigid local systems I Ã¢â‚¬â€œ 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 HodgeÃ¢â‚¬â€œde Rham theory of modular groups R. Hain.