Lecture notes for graduates or researchers wishing to enter this modern field of research.

The main goal of the CIME Summer School on "Algebraic Cycles and Hodge Theory" has been to gather the most active mathematicians in this area to make the point

In its simplest form, Hodge theory is the study of periods – integrals of algebraic differential forms which arise in the study of complex geometry and moduli

This is the first detailed elementary introduction to Galois cohomology and its applications. The introductory section is self-contained and provides the basic

This book introduces a new approach to building models of bounded arithmetic, with techniques drawn from recent results in computational complexity. Proposition