Preface ....................................................... vii
Introduction ................................................... ix
List of Conference Participants ................................ xv
PART I. HODGE THEORY AT THE BOUNDARY
I.A. PERIOD DOMAINS AND THEIR COMPACTIFICATIONS
1 Classical Period Domains ..................................... 3
Radu Laza and Zheng Zhang
2 The singularities of the invariant metric on the Jacobi
line bundle ................................................. 45
Jose Ignacio Burgos Gil, Jurg Kramer, and Ulf Kühn
3 Symmetries of Graded Polarized Mixed Hodge Structures ....... 78
Aroldo Kaplan
I.B. PERIOD MAPS AND ALGEBRAIC GEOMETRY
4 Deformation theory and limiting mixed Hodge structures ...... 88
Mark Green and Phillip Griffiths
5 Studies of closed/open mirror symmetry for quintic
threefolds through log mixed Hodge theory .................. 134
Sampei Usui
6 The 14th case VHS via К3 fibrations ........................ 165
Adrian Clingher, Charles F. Doran, Jacob Lewis, Andrey
Y. Novoseltsev, and Alan Thompson
PART II. ALGEBRAIC CYCLES AND NORMAL FUNCTIONS
7 A simple construction of regulator indecomposable higher
Chow cycles in elliptic surfaces ........................... 231
Masanori Asakura
8 A relative version of the Beilinson-Hodge conjecture ....... 241
Rob de Jeu, James D. Lewis, and Deepam Patel
9 Normal functions and spread of zero locus .................. 264
Morihiko Saito
10 Fields of definition of Hodge loci ......................... 275
Morihiko Saito and Christian Schnell
11 Tate twists of Hodge structures arising from abelian
varieties .................................................. 292
Salman Abdulali
12 Some surfaces of general type for which Bloch's
conjecture holds ........................................... 308
C. Pedrini and C. Weibel
PART III. THE ARITHMETIC OF PERIODS
III.A. MOTIVES, GALOIS REPRESENTATIONS, AND AUTOMORPHIC FORMS
13 An introduction to the Langlands correspondence ............ 333
Wushi Goldring
14 Generalized Kuga-Satake theory and rigid local systems I:
the middle convolution ..................................... 368
Stefan Patrikis
15 On the fundamental periods of a motive ..................... 393
Hiroyuki Yoshida
III.B. MODULAR FORMS AND ITERATED INTEGRALS
16 Geometric Hodge structures with prescribed Hodge numbers ... 414
Donu Arapura
17 The Hodge-de Rham Theory of Modular Groups ................. 422
Richard Hain
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