This volume contains papers by invited speakers at the International Colloquium co-sponsored by the International Mathematical Union on Algebra, Arithmetic and Geometry held at the Tata Institute of Foundational Research, Mumbai, presenting latest developments.

Part I: Symplectic Groups and Permutation Polynomials, Part I / Homological Criteria for Regular Homomorphisms and for Locally Complete Intersection Homomorphisms / Norm Principle for Reductive Algebraic Groups / On Euler Classes and Stably Free Projective Modules / HigherAbel-Jacobi Maps / Enriched Hodge Structures / Quadratic Forms Over Fraction Fields of Two-dimensional Henselian Rings and Brauer Groups of Related Schemes / Semi-topological K-theory of Real Varieties Part II: Sequentially Cohen-Macaulay Modules and Local Cohomology / From Mennicke Symbols to Euler Class Groups / On Generic Triality / On the Harder-Narasimhan Filtration of Principal Bundles / Geometry of Low Height Representations / Generalized Jacobian Conjucture and Related Topics / Construction of Rank Two Vector Bundles on Projective Spaces / Constructible Sheaves / Cancellation Problem for Projective Modules Over Certain Affine Algebras / Self-dual Algebraic Varieties and Nilpotent Orbits / Intersection Multiplicities and Dimension Inequalities / Some Formal Aspects of the Theorems of Mumford-Ramanujam / Euler-Poincare Characteristics of p-adic Lie Groups and Arithmetic / On the Vanishing of H3 (SL2(A,I), Z/l)

Graduate and Postgraduate students of Colleges and Universities