Explains, using examples, the central role of the fundamental group in the geometry, global analysis, and topology of manifolds.

Intersection theory has played a prominent role in the study of closed symplectic 4-manifolds since Gromov's famous 1985 paper on pseudoholomorphic curves, lead

Provides a comprehensive introduction to the theory of random orthogonal, unitary, and symplectic matrices.

The Mordell conjecture (Faltings's theorem) is one of the most important achievements in Diophantine geometry, stating that an algebraic curve of genus at least

This authoritative volume in honor of Alain Connes, the foremost architect of Noncommutative Geometry, presents the state-of-the art in the subject. The book fe