Volume I

Preface

Gavril Farkas and Ian Morrison

Logarithmic geometry and moduli

Dan Abramovich, Qile Chen, Danny Gillam, Yuhao Huang, Martin Olsson, Matthew Satriano and Shenghao Sun

Invariant Hilbert schemes

Michel Brion

Algebraic and tropical curves: comparing their moduli spaces

Lucia Caporaso

A superficial working guide to deformations and moduli

F. Catanese

Moduli spaces of hyperbolic surfaces and their Weil–Petersson volumes

Norman Do

Equivariant geometry and the cohomology of the moduli space of curves

Dan Edidin

Tautological and non-tautological cohomology of the moduli space of curves

C. Faber and R. Pandharipande

Alternate compactifications of moduli spaces of curves

Maksym Fedorchuk and David Ishii Smyth

The cohomology of the moduli space of Abelian varieties

Gerard van der Geer

Moduli of K3 surfaces and irreducible symplectic manifolds

V. Gritsenko, K. Hulek and G.K. Sankaran

Normal functions and the geometry of moduli spaces of curves

Richard Hain

Volume II

Parameter spaces of curves

Joe Harris

Global topology of the Hitchin system

Tás Hausel

Differential forms on singular spaces, the minimal model program, and hyperbolicity of moduli stacks

Stefan Kebekus

Contractible extremal rays on \(\mathcal{M}_{0,n}\)

Seán Keel and James McKernan

Moduli of varieties of general type

János Kollár

Singularities of stable varieties

Sándor J Kovács

Soliton equations and the Riemann-Schottky problem

I. Krichever and T. Shiota

GIT and moduli with a twist

Radu Laza

Good degenerations of moduli spaces

Jun Li

Localization in Gromov-Witten theory and Orbifold Gromov-Witten theory

Chiu-Chu Melissa Liu

From WZW models to modular functors

Eduard Looijenga

Shimura varieties and moduli

J.S. Milne

The Torelli locus and special subvarieties

Ben Moonen and Frans Oort

Volume III

Birational geometry for nilpotent orbits

Yoshinori Namikawa

Cell decompositions of moduli space, lattice points and Hurwitz problems

Paul Norbury

Moduli of abelian varieties in mixed and in positive characteristic

Frans Oort

Local models of Shimura varieties, I: Geometry and combinatorics

Georgios Pappas, Michael Rapoport and Brian Smithling

Generalized theta linear series on moduli spaces of vector bundles on curves

Mihnea Popa

Computer aided unirationality proofs of moduli spaces

Frank-Olaf Schreyer

Deformation theory from the point of view of fibered categories

Mattia Talpo and Angelo Vistoli

Mumford’s conjecture — a topological outlook

Ulrike Tillmann

Rational parametrizations of moduli spaces of curves

Alessandro Verra

Hodge loci

Claire Voisin

Homological stability for mapping class groups of surfaces

Nathalie Wahl