Preface; Contents; On the Kobayashi Pseudometric, Complex Automorphisms and Hyperkähler Manifolds; 1 Introduction; 2 Preliminaries; 3 (Royden
)Kobayashi Pseudometric on Abelian Fibrations; 4 Automorphisms of Infinite Order; 5 Metric Geometry of Kobayashi Quotients; 6 Eigenvalues and Periodic Points of Hyperbolic Automorphisms; References; Lines on Cubic Hypersurfaces Over Finite Fields; 1 Introduction; 2 Definitions and Tools; 2.1 The Weil and Tate Conjectures; 2.2 The Katz Trace Formula; 2.3 The Galkin
Shinder Formulas; 2.4 Abelian Varieties Over Finite Fields; 3 Cubic Surfaces.

4 Cubic Threefolds4.1 The Zeta Function of the Surface of Lines; 4.2 Existence of Lines on Smooth Cubic Threefolds Over Large Finite Fields; 4.3 Computing Techniques: The Bombieri
Swinnerton-Dyer Method; 4.4 Lines on Mildly Singular Cubic Threefolds; 4.5 Examples of Cubic Threefolds; 4.6 Average Number of Lines; 5 Cubic Fourfolds; 5.1 The Zeta Function of the Fourfold of Lines; 5.2 Existence of Lines over Large Finite Fields; 5.3 Existence of Lines over Some Finite Fields; 5.4 Examples of Cubic Fourfolds; 6 Cubics of Dimensions 5 or More; References.

Perverse Sheaves of Categories and Non-rationality1 Introduction; 2 Perverse Sheaves of Categories; 2.1 Definitions; 2.2 Some More Examples; 3 Deformations of Perverse Sheaves of Categories and Poisson Deformations; 3.1 Warmup: Deformations of mathbbP2; 3.2 Noncommutative Deformations of mathbbP3; 3.3 Perverse Sheaves of Categories and Elliptic Curves; 4 Landau
Ginzburg Model Computations for Threefolds; 4.1 The LG Model of a Quartic Double Solid; 4.2 Torsion in Cohomology of the LG Model; 4.3 The Cubic Threefold; 4.4 The Quartic Double Fourfold; 4.5 Base Change and Torsion.

1.2 Morphisms to Brauer
Severi Varieties.