Contents:

• Algebraic Geometry:
• The Hasse-Witt Matrix of an Algebraic Curve
• Rational Points of Algebraic Curves over Functional Fields
• Correspondences, Motives, and Monoidal Transformations
• New Directions in Geometry
• Arrangements of Hyperplanes, Higher Braid Groups and Higher Bruhat Orders
• Modular Forms and Diophantine Equations:
• The p-Torsion of Elliptic Curves is Uniformly Bounded
• Parabolic Points and Zeta-Functions of Modular Curves
• Periods of p-Adic Schottky Groups
• Rational Points of Bounded Height on Fano Varieties
• Points of Bounded Height on del Pezzo Surfaces
• Differential Equations and Mathematical Physics:
• Conservation Laws and Lax Representation of Benney's Long Wave Equations
• Gelfand–Dikii Hamiltonian Operator and the Coadjoint Representation of the Volterra Group
• The Twistor Transformation and Algebraic–Geometric Constructions of Solutions of the Equations of Field Theory
• The Mumford Form and the Polyakov Measure in String Theory
• and other papers