Editor of Duke Mathematical Journal wins Chern Medal Award

DMJ_163_8Congratulations to Duke Mathematical Journal editor Phillip Griffiths! He was awarded the 2014 Chern Medal for his work in complex geometry, particularly his work in Hodge theory and periods of algebraic varieties. The prize is given at the International Congress of Mathematicians, which is being held currently in Seoul, South Korea.

To read the official press release, click here.

Several contributors to DMJ have also been awarded the Fields Medal, including Maryam Mirzakhani, the first woman to win the medal. Other winners include Artur Avila and Manjul Bhargava. See a list of their contributions to DMJ below. Congratulations to all!

For more information on Duke Mathematical Journal, visit dukeupress.edu/dmj.

Contributions to DMJ from Fields Medalists include:

Maryam Mirzakhani, co-author of "Lattice point asymptotics and volume growth on Teichmüller space," here; Artur Avila, co-author of "Cohomological equations and invariant distributions for minimal circle diffeomorphisms," here and "Generic Singular Spectrum For Ergodic Schrödinger Operators," here; and Manjul Bhargava, co-author of "Error estimates for the Davenport-Heilbronn theorems," here.

One comment

  1. sure asa say prof dr mircea orasanu and prof horia orasanu the above are very important in applications as followings
    GEOMETRIC FORMULATION OF MECHANICAL SYSTEMS
    SUBJECTED TO CONSTRAINTS
    Author Horia Orasanu
    ABSTRACT
    Complex systems are large interdisciplinary research topics that have been studied by means of a mixed basic theory that mainly derives from physics and computer simulation. Such systems are made of many interacting elementary units that are called “agents”.
    The way in which such a system manifests itself cannot be exclusively predicted only by the behavior of individual elements. Its manifestation is also induced by the manner in which the elements relate in order to influence global behavior.
    1 INTRODUCTION

    The most significant properties of complex systems are emergence, self-organization, adaptability, etc. [1–4].
    Examples of complex systems can be found in human societies, brains, the Internet, ecosystems, biological evolution, stock markets, economies and many others [1, 2]. Particularly, polymers are examples of such complex systems. Their forms include a multitude of organizations starting from simple, linear chains of identical structural units and ending with very complex chains consisting of sequences of amino acids that form the building blocks of living fields. One of the most intriguing polymers in nature is DNA, which creates cells by means of a simple, but very elegant language. It is responsible for the remarkable way in which individual cells organize into complex systems, such as organs, which, in turn, form even more complex systems, such as organisms. The study of complex systems can offer a glimpse into the realistic dynamics of polymers and solve certain difficult problems (protein folding) [1–4].
    2 FORMULATION

    Correspondingly, theoretical models that describe the dynamics of complex systems are sophisticated [1–4]. However, the situation can be standardized taking into account that the complexity of interaction processes imposes various temporal resolution scales, while pattern evolution implies different freedom degrees [5].
    In order to develop new theoretical models, we must admit that complex systems displaying chaotic behavior acquire self-similarity (space-time structures seem to appear) in association with strong fluctuations at all possible space-time scales [1–4]. Then, in the case of temporal scales that are large with respect to the inverse of the highest Lyapunov exponent, the deterministic trajectories are replaced by a collection of potential trajectories, while the concept of definite positions by that of probability density. One of the most interesting examples is the collision process in complex systems, a case in which the dynamics of the particles can be described by non-differentiable curves.
    Since non-differentiability appears as the universal property of complex systems, it is necessary to construct a non-differentiable physics. Thus, the complexity of the interaction processes is replaced by non-differentiability; accordingly, it is no longer necessary to use the whole classical “arsenal” of quantities from standard physics (differentiable physics).
    This topic was developed within scale relativity theory (SRT) [6,7] and non-standard scale relativity theory (NSSRT) [8–22]. In this case, we assume that the movements of complex system entities take place on continuous, but non-differentiable, curves (fractal curves), so that all physical phenomena involved in the dynamics depend not only on space-time coordinates, but also on space-time scale resolution. From such a perspective, physical quantities describing the dynamics of complex systems may be considered fractal functions [6,7]. Moreover, the entities of the complex system may be reduced to and identified with their own trajectories, so that the complex system will behave as a special fluid lacking interaction (via their geodesics in a non-differentiable (fractal) space). We have called such fluid a “fractal fluid” [8–22].

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    © 2014 by the authors; licensee MDPI, Basel, Switzerland This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/4.0/).

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