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Forme differenziali e loro integrali by B. Segre Pdf
G. De Rham: La théorie des formes différentiielles extérieures et l ́homologie des variétés différentiablles.- G. Fichera: Teoria assiomatica delle forme armoniche.- W.V.D. Hodge: Differential forms in algebraic geometry.- D.B. Scott: Correspondences between algebraic surfaces.- P.Dolbeault: Sur le groupe de cohomologie entière de dimension d ́une variété analytique complexe.- E. Kähler: Der innere Differentialkalkül.
Algebraic Geometry between Tradition and Future by Gilberto Bini Pdf
An incredible season for algebraic geometry flourished in Italy between 1860, when Luigi Cremona was assigned the chair of Geometria Superiore in Bologna, and 1959, when Francesco Severi published the last volume of the treatise on algebraic systems over a surface and an algebraic variety. This century-long season has had a prominent influence on the evolution of complex algebraic geometry - both at the national and international levels - and still inspires modern research in the area. "Algebraic geometry in Italy between tradition and future" is a collection of contributions aiming at presenting some of these powerful ideas and their connection to contemporary and, if possible, future developments, such as Cremonian transformations, birational classification of high-dimensional varieties starting from Gino Fano, the life and works of Guido Castelnuovo, Francesco Severi's mathematical library, etc. The presentation is enriched by the viewpoint of various researchers of the history of mathematics, who describe the cultural milieu and tell about the bios of some of the most famous mathematicians of those times.
Some Properties of Differentiable Varieties and Transformations by Beniamino Segre Pdf
The present volume contains, together with numerous additions and extensions, the course of lectures which I gave at Pavia (26 September till 5 October 1955) by invitation of the «Centro Internazionale Mate matico Estivo». The treatment has the character of a monograph, and presents various novel features, both in form and in substance; these are indicated in the notes which will be found at the beginning and end of each chapter. Of the nine parts into which the work is divided, the first four are essentially differential in character, the next three deal with algebraic geometry, while the last two are concerned with certain aspects of the theory of differential equations and of correspondences between topo logical varieties. A glance at the index will suffice to give a more exact idea of the range and variety of the contents, whose chief characteristic is that of establishing suggestive and sometimes unforeseen relations between apparently diverse subjects (e. g. differential geometry in the small and also in the large, algebraic geometry, function theory, topo logy, etc.); prominence is given throughout to the geometrical viewpoint, and tedious calculations are as far as possible avoided.
Enumerative Invariants in Algebraic Geometry and String Theory by Marcos Marino,Michael Thaddeus,Ravi Vakil Pdf
Starting in the middle of the 80s, there has been a growing and fruitful interaction between algebraic geometry and certain areas of theoretical high-energy physics, especially the various versions of string theory. Physical heuristics have provided inspiration for new mathematical definitions (such as that of Gromov-Witten invariants) leading in turn to the solution of problems in enumerative geometry. Conversely, the availability of mathematically rigorous definitions and theorems has benefited the physics research by providing the required evidence in fields where experimental testing seems problematic. The aim of this volume, a result of the CIME Summer School held in Cetraro, Italy, in 2005, is to cover part of the most recent and interesting findings in this subject.
Optimal Transportation and Applications by Luigi Ambrosio Pdf
Leading researchers in the field of Optimal Transportation, with different views and perspectives, contribute to this Summer School volume: Monge-Ampère and Monge-Kantorovich theory, shape optimization and mass transportation are linked, among others, to applications in fluid mechanics granular material physics and statistical mechanics, emphasizing the attractiveness of the subject from both a theoretical and applied point of view. The volume is designed to become a guide to researchers willing to enter into this challenging and useful theory.
Filtration in Porous Media and Industrial Application by M.S. Espedal,A. Fasano,A. Mikelic Pdf
This book is devoted to the presentation of some flow problems in porous media having relevant industrial applications. The main topics covered are: the manufacturing of composite materials, the espresso coffee brewing process, the filtration of liquids through diapers, various questions about flow problems in oil reservoirs and the theory of homogenization. The aim is to show that filtration problems arising in very practical industrial context exhibit interesting and highly nontrivial mathematical aspects. Thus the style of the book is mathematically rigorous, but specifically oriented towards applications, so that it is intended for both applied mathematicians and researchers in various areas of technological interest. The reader is required to have a good knowledge of the classical theory of PDE and basic functional analysis.
Mathematical Aspects of Evolving Interfaces by Luigi Ambrosio,Klaus Deckelnick,Gerhard Dziuk,Masayasu Mimura,Vsvolod Solonnikov,Halil Mete Soner Pdf
Interfaces are geometrical objects modelling free or moving boundaries and arise in a wide range of phase change problems in physical and biological sciences, particularly in material technology and in dynamics of patterns. Especially in the end of last century, the study of evolving interfaces in a number of applied fields becomes increasingly important, so that the possibility of describing their dynamics through suitable mathematical models became one of the most challenging and interdisciplinary problems in applied mathematics. The 2000 Madeira school reported on mathematical advances in some theoretical, modelling and numerical issues concerned with dynamics of interfaces and free boundaries. Specifically, the five courses dealt with an assessment of recent results on the optimal transportation problem, the numerical approximation of moving fronts evolving by mean curvature, the dynamics of patterns and interfaces in some reaction-diffusion systems with chemical-biological applications, evolutionary free boundary problems of parabolic type or for Navier-Stokes equations, and a variational approach to evolution problems for the Ginzburg-Landau functional.
Optimal Shape Design by B. Kawohl,O. Pironneau,L. Tartar,J.-P. Zolesio Pdf
Optimal Shape Design is concerned with the optimization of some performance criterion dependent (besides the constraints of the problem) on the "shape" of some region. The main topics covered are: the optimal design of a geometrical object, for instance a wing, moving in a fluid; the optimal shape of a region (a harbor), given suitable constraints on the size of the entrance to the harbor, subject to incoming waves; the optimal design of some electrical device subject to constraints on the performance. The aim is to show that Optimal Shape Design, besides its interesting industrial applications, possesses nontrivial mathematical aspects. The main theoretical tools developed here are the homogenization method and domain variations in PDE. The style is mathematically rigorous, but specifically oriented towards applications, and it is intended for both pure and applied mathematicians. The reader is required to know classical PDE theory and basic functional analysis.
Noncommutative Geometry by Alain Connes,Joachim Cuntz,Erik G. Guentner,Nigel Higson,Jerome Kaminker,John E. Roberts Pdf
Noncommutative Geometry is one of the most deep and vital research subjects of present-day Mathematics. Its development, mainly due to Alain Connes, is providing an increasing number of applications and deeper insights for instance in Foliations, K-Theory, Index Theory, Number Theory but also in Quantum Physics of elementary particles. The purpose of the Summer School in Martina Franca was to offer a fresh invitation to the subject and closely related topics; the contributions in this volume include the four main lectures, cover advanced developments and are delivered by prominent specialists.
Iwahori-Hecke Algebras and their Representation Theory by Ivan Cherednik,Yavor Markov,Roger E. Howe,George Lusztig Pdf
Two basic problems of representation theory are to classify irreducible representations and decompose representations occuring naturally in some other context. Algebras of Iwahori-Hecke type are one of the tools and were, probably, first considered in the context of representation theory of finite groups of Lie type. This volume consists of notes of the courses on Iwahori-Hecke algebras and their representation theory, given during the CIME summer school which took place in 1999 in Martina Franca, Italy.
Computational Mathematics Driven by Industrial Problems by R. Burkard,P. Deuflhard,A. Jameson,J.-L. Lions,G. Strang Pdf
These lecture notes by very authoritative scientists survey recent advances of mathematics driven by industrial application showing not only how mathematics is applied to industry but also how mathematics has drawn benefit from interaction with real-word problems. The famous David Report underlines that innovative high technology depends crucially for its development on innovation in mathematics. The speakers include three recent presidents of ECMI, one of ECCOMAS (in Europe) and the president of SIAM.
Pseudo-Differential Operators by Hans G. Feichtinger,Bernard Helffer,Michael Lamoureux,Nicolas Lerner,Joachim Toft Pdf
Pseudo-differential operators were initiated by Kohn, Nirenberg and Hörmander in the sixties of the last century. Beside applications in the general theory of partial differential equations, they have their roots also in the study of quantization first envisaged by Hermann Weyl thirty years earlier. Thanks to the understanding of the connections of wavelets with other branches of mathematical analysis, quantum physics and engineering, such operators have been used under different names as mathematical models in signal analysis since the last decade of the last century. The volume investigates the mathematics of quantization and signals in the context of pseudo-differential operators, Weyl transforms, Daubechies operators, Wick quantization and time-frequency localization operators. Applications to quantization, signal analysis and the modern theory of PDE are highlighted.
