Corrado De Concini's Books

Topics in Hyperplane Arrangements, Polytopes and Box-Splines brings together many areas of research that focus on methods to compute the number of integral points in suitable families or variable polytopes. The topics introduced expand upon differential and difference equations, approximation theory, cohomology, and module theory. This book, written by two distinguished authors, engages a broad audience by proving the a strong foudation. This book may be used in the classroom setting as well as a reference for researchers.

CONTENTS: L. Boutet de Monvel: Indice de systemes differentiels.- C. De Concini, C. Procesi: Quantum groups.- P. Schapira, J.P. Schneiders: Index theorems for R-constructible sheaves and for D-modules.- N. Berline, M. Vergne: The equivariant Chern character and index of G-invariant operators.

Rovereto,December2002 CorradoPriami ProgrammeCommitteeofCMSB 2003 CorradoPriami(Chair),UniversityofTrento(Italy), CharlesAu?ray,CNRS,Villejuif(France), CosimaBaldari,Universit`adiSiena(Italy), AlexanderBockmayr,Universit ́eHenriPoincar ́e(France), LucaCardelli,MicrosoftResearchCambridge(UK), VincentDanos,Universit ́eParisVII(France), PierpaoloDegano,Universitad ` iPisa(Italy), Francois ̧ Fages,INRIA,Rocquencourt(France), DrabløsFinn,NorwegianUniversityofScienceandTechnology,Trondheim(N- way), MonikaHeiner,BrandenburgUniversityofTechnologyatCottbus(Germany), InaKoch,UniversityofAppliedSciencesBerlin,(Germany), JohnE.

This book gives a unified, complete, and self-contained exposition of the main algebraic theorems of invariant theory for matrices in a characteristic free approach. More precisely, it contains the description of polynomial functions in several variables on the set of matrices with coefficients in an infinite field or even the ring of integers, invariant under simultaneous conjugation. Following Hermann Weyl's classical approach, the ring of invariants is described by formulating and proving (1) the first fundamental theorem that describes a set of generators in the ring of invariants, and (2) the second fundamental theorem that describes relations between these generators. The authors study both the case of matrices over a field of characteristic 0 and the case of matrices over a field of positive characteristic. While the case of characteristic 0 can be treated following a classical approach, the case of positive characteristic (developed by Donkin and Zubkov) is much harder. A presentation of this case requires the development of a collection of tools. These tools and their application to the study of invariants are exlained in an elementary, self-contained way in the book.

Book's by Corrado De Concini

Topics in Hyperplane Arrangements, Polytopes and Box-Splines

Topics in Hyperplane Arrangements, Polytopes and Box-Splines

D-modules, Representation Theory, and Quantum Groups

D-modules, Representation Theory, and Quantum Groups

Computational Methods in Systems Biology

Computational Methods in Systems Biology

The Invariant Theory of Matrices

The Invariant Theory of Matrices

D-modules, Representation Theory, and Quantum Groups

D-modules, Representation Theory, and Quantum Groups

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