Mostrando recursos 1 - 20 de 92

  1. Moduli spaces of stable sheaves on schemes: restriction theorems, boundedness and the GIT construction

    Maruyama, Masaki
    Chapter I: First we shall show that if we collect all the vector bundles on a projective variety and require a weak universal property of a moduli space, then there does not exist the moduli space. This motivates us to introduce the notion of stability and semi-stability. The idea of Harder-Narasimhan filtration plays a crucial role sometimes behind strong results and sometimes very explicitly. Two of basic results on boundedness are proved in the section 3. The formulation of the first is due to L. S. Kleiman and the second is a theorem of Grothendieck. We shall show a beautiful...

  2. Discrete Geometric Analysis

    Barlow, Martin T.; Jordán, Tibor; Zuk, Andrzej
    This is a volume of lecture notes based on three series of lectures given by three visiting professors of RIMS, Kyoto University during the year long project research "Discrete Geometric Analysis" in the Japanese academic year 2012. The aim of the project research was to make comprehensive research on topics related to discreteness in geometry, analysis and optimization. The goal is to expand and make a new stream of discrete geometric analysis by exchanging ideas in each area. The main themes during the project and also of this volume are threefold: i) Discrete probability theory and analysis on graphs, ii)...

  3. III – Analysis and Geometry on Groups

    Zuk, Andrzej
    These notes present different aspects of analysis and geometry on infinite groups. They are centered around two notions, amenability and property (T), which play a central role both from geometric and analytic point of view. We analyze these notions with their relation to expander graphs constructions.

  4. II – Combinatorial Rigidity: Graphs and Matroids in the Theory of Rigid Frameworks

    Jordán, Tibor
    This paper is based on material presented at the Research Institute for Mathematical Sciences (RIMS), Kyoto University, in October 2012 in a series of lectures. Thus, on one hand, it serves as the lecture note of this minicourse Combinatorial rigidity: graphs and matroids in the theory of rigid frameworks. On the other hand, this final, extended form is perhaps closer to a short monograph on combinatorial rigidity problems of two-dimensional frameworks. It contains the fundamental results of this area as well as a number of more recent results concerning extensions, variations and applications. Also added are several exercises and some...

  5. I – Loop Erased Walks and Uniform Spanning Trees

    Barlow, Martin T.

  6. A Beginner's Guide to the Theory of Viscosity Solutions

    Koike, Shigeaki

  7. Godbillon-Vey Class of Transversely Holomorphic Foliations

    Asuke, Taro
    This volume provides a study of the Godbillon–Vey class and other real secondary characteristic classes of transversely holomorphic foliations. One of the main tools in the study is complex secondary characteristic classes. Intended to be self-contained and introductory, this volume contains a brief survey of the theory of secondary characteristic classes of transversely holomorphic foliations. A construction of secondary characteristic classes of families of such foliations is also included. By means of these classes, new proofs of the rigidity of the Godbillon–Vey class in the category of transversely holomorphic foliations are given.

  8. Geometric Structures on 2-Orbifolds: Exploration of Discrete Symmetry

    Choi, Suhyoung
    This book exposes the connection between the low-dimensional orbifold theory and geometry that was first discovered by Thurston in 1970s providing a key tool in his proof of the hyperbolization of Haken 3-manifolds. Our main aims are to explain most of the topology of orbifolds but to explain the geometric structure theory only for 2-dimensional orbifolds, including their Teichmüller (Fricke) spaces. We tried to collect the theory of orbifolds scattered in various literatures for our purposes. Here, we set out to write down the traditional approach to orbifolds using charts, and we include the categorical definition using groupoids. We will...

  9. Hierarchy of Semiconductor Equations: Relaxation Limits with Initial Layers for Large Initial Data

    Nishibata, Shinya; Suzuki, Masahiro
    This volume provides a recent study of mathematical research on semiconductor equations. With recent developments in semiconductor technology, several mathematical models have been established to analyze and to simulate the behavior of electron flow in semiconductor devices. Among them, a hydrodynamic, an energy-transport and a drift-diffusion models are frequently used for the device simulation with the suitable choice, depending on the purpose of the device usage. Hence, it is interesting and important not only in mathematics but also in engineering to study a model hierarchy, relations among these models. The model hierarchy has been formally understood by relaxation limits letting...

  10. Monte Carlo Method, Random Number, and Pseudorandom Number

    Sugita, Hiroshi
    Although the Monte Carlo method is used in so many fields, its mathematical foundation has been weak until now because of the fundamental problem that a computer cannot generate random numbers. This book presents a strong mathematical formulation of the Monte Carlo method which is based on the theory of random number by Kolmogorov and others and that of pseudorandom number by Blum and others. As a result, we see that the Monte Carlo method may not need random numbers and pseudorandom numbers may suffice. In particular, for the Monte Carlo integration, there exist pseudorandom numbers which serve as complete...

  11. Kähler Geometry of Loop Spaces

    Sergeev, Armen
    In this book we study three important classes of infinite-dimensional Kähler manifolds — loop spaces of compact Lie groups, Teichmüller spaces of complex structures on loop spaces, and Grassmannians of Hilbert spaces. Each of these manifolds has a rich Kähler geometry, considered in the first part of the book, and may be considered as a universal object in a category, containing all its finite-dimensional counterparts. ¶On the other hand, these manifolds are closely related to string theory. This motivates our interest in their geometric quantization presented in the second part of the book together with a brief survey of geometric quantization...

  12. Algebraic and Analytic Aspects of Zeta Functions and $L$-functions

    This volume contains lectures presented at the French–Japanese Winter School on Zeta and $L$-functions, held at Muira, Japan, 2008. The main aim of the School was to study various aspects of zeta and $L$-functions with special emphasis on recent developments. A series of detailed lectures were given by experts in topics that include height zeta-functions, spherical functions and Igusa zeta-functions, multiple zeta values and multiple zeta-functions, classes of Euler products of zeta-functions, and $L$-functions associated with modular forms. This volume should be helpful to future generations in their study of the fascinating theory of zeta and $L$-functions.

  13. Part VIII. Hypergeometric constructions of rational approximations for (multiple) zeta values

    Rivoal, Tanguy

  14. Part VII. An introduction to $p$-adic and motivic zeta functions and the monodromy conjecture

    Nicaise, Johannes

  15. Part VI. An introduction to the theory of zeta-functions of root systems

    Komori, Yasushi; Matsumoto, Kohji; Tsumura, Hirofumi

  16. Part V. Rankin-Selberg method and periods of modular forms

    Katsurada, Hidenori

  17. Part IV. Poly-Bernoulli numbers and related zeta functions

    Kaneko, Masanobu

  18. Part III. Spherical functions on $p$-adic homogeneous spaces

    Hironaka, Yumiko

  19. Part II. Lectures on height zeta functions: At the confluence of algebraic geometry, algebraic number theory, and analysis

    Chambert-Loir, Antoine

  20. Part I. Analytic continuation of some zeta functions

    Bhowmik, Gautami

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