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

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

    Choi, Suhyoung

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

    Nishibata, Shinya; Suzuki, Masahiro

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

    Sugita, Hiroshi

  11. Kähler Geometry of Loop Spaces

    Sergeev, Armen

  12. Algebraic and Analytic Aspects of Zeta Functions 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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