Algebra Arithmetic and Geometry with Applications : Papers from Shreeram S. Abhyankar’s 70th Birthday Conference This volume is the proceedings of the Conference on Algebra and Algebraic Geometry with Applications which was held July 19 – 26 2000 at Purdue University to honor Professor Shreeram S. Abhyankar on the occasion of his seventieth birthday. Eighty five of Professor Abhyankars students collaborators and colleagues were invited participants. Sixty participants presented papers related to Professor Abhyankars broad areas of mathematical interest. There were sessions on algebraic geometry singularities group theory Galois theory combinatorics Drinfield modules affine geometry and the Jacobian problem. This volume offers an outstanding collection of papers by authors who are among the experts in their areas. Preface A Robust Computationally Efficient Methodology to Set Service Levels for Components in Assemble to Order Environments Smale Strategies for Prisoner’s Dilemma Type Games Remembrances of Prof. Shreeram S. Abhyankar and ABC of Singularities Thoughts on Symplectic Groups and Symplectic Equations Field Generators for the Quantum Plane Bounding Singular Surfaces of General Type Toric Modifications of Free Toric Varieties Recent Remarks on Analytical Equivalence Behavior of the Torsion of the Differential Module of an Algebroid Curve Under Quadratic Transformations Note on Equisingularity in Codimension 1 and Characteristic p  = 0 Toric Structure of the Graded Algebra Relative to a Valuation Postulation of Adjoint Ideals and Geometry of Projective Curves Belghitti Gruson or Semple 2S4*Q8 extensions The Structure of Morphisms Around the Abhyankar Moh Theorem PSL2(11) is Admissible for all Number Fields Adjoints and Max Noether’s Fundamentalsatz Continuity Loci for Polynomial Systems Asymptotically Optimal Towers of Curves over Finite Fields The Hilbert Series of Pfaffian Rings The Impact of the Infinite Primes on the Riemann Hypothesis for Characteristic p Valued L series General Elements of Complete Ideals and Valuations Centered at a Two dimensional Regular Local Ring Exceptional Polynomials over Arbitrary Fields Abhyankar’s Local Conjecture on Fundamental Groups Questions of Connectedness of the Hilbert Scheme of Curves in 3 Catenary Local Rings with Geometrically Normal Formal Fibers Diamond Closure A Determinantal Formula for the Hilbert Series of One sided Ladder Determinantal Rings Multiplicities of Singular Points in Schubert Varieties of Grassmannians Geometric Applications of the Residue Theorem on Algebraic Curves On p Groups in Characteristic p Degree Two Generalized Iteration of q Additive Polynomials Wild Singularites on the Fermat Curve over Z Algebraic Curves over F3 with Many Rational Points Gröbner Bases of Symmetric Quotients and Applications Abstract Embeddings of Concrete Matrix Groups Some Generalization of Melville Theorem Multiple Planes Ramified over One place Curves An Application of Generalized Newton Puiseux Expansions Elliptic Subfields and Automorphisms of Genus 2 Function Fields Some Ideas in the Classification of the Finite Simple Groups Abhyankar’s Nice Equations The Scientific WorkPlace Computational Interface Diophantine Approximation in Finite Characteristic Puiseux Expansions in Nonzero Characteristic Arithmetical Geometrical Galois Representations and the Inverse Galois Problem Polynomials and Power Series Author Index.