Cornell's Fifth Conference on Analysis, Probability and Mathematical Physics on Fractals

第五届分析、概率和数学物理会议将于2014年6月11日至15日在康奈尔大学数学系举行。在当前的数学研究中，分形图的出现方式有很多种。本次会议的主题是那些底层空间是分形的，研究的主题包括微分方程的模拟、随机过程以及在这些分形空间上发生的物理相互作用的模型。由于Barlow、Perkins、Bass、Kusuoka、周和Kigami的开创性工作，为讨论这类问题提供了一个完善的、严格的数学框架。这次会议将有助于研究无序介质中的过程(分形学)，这一过程在物理、化学、生物科学和工程中有许多应用。渗流簇中的扩散过程、分形物体的振动、带有随机障碍物的通道中的信号传播、分形天线中的电磁波、海洋学中的Rossby波、金融市场模型、神经结构只是这些过程的许多例子中的一小部分。有许多重要的科学问题涉及到在分形空间上对物理系统进行建模。理论物理学家的参与有助于促进对这些领域感兴趣的数学和物理界之间日益增长的互动。这次会议将有助于向物理界通报数学家正在开发的基础设施，并将就其他科学家的兴趣和问题向数学家提供有趣的反馈。这些康奈尔会议从2002年开始每三年举行一次。这一系列的前四次会议对这些领域的发展产生了重大影响，将相关学科的主要贡献者、青年研究人员和数学家聚集在一起，了解最近的工作并规划联合项目。预计第五届会议将延续这一传统。为期五天的会议将分为三个部分：上午由该领域的主要研究人员进行半小时的演讲，描述最近的重要进展；下午早些时候举行小型课程，使高级本科生、研究生和相关领域的研究人员能够学习该领域的一些基础知识，并讨论重要的公开问题；以及在下午晚些时候的平行会议上进行20分钟的演讲，允许所有与会者展示他们的研究成果。会议的一个重要部分是迷你课程，主要是针对未来数学家的培训。大量初级研究人员，包括少数族裔、代表性不足的群体成员和康奈尔大学和康涅狄格大学REU项目的本科生，预计将从这些课程中受益。

The fifth Conference on Analysis, Probability and Mathematical Physics on Fractals will be held at Cornell University Mathematics Department from June 11-15, 2014. There are many ways in which fractals appear in current mathematical research. The topics of this conference are those where the underlying space is fractal, and the subjects studied include the analogs of differential equations, random processes and models of physical interactions taking place on these fractal spaces. Due to the pioneering work of Barlow, Perkins, Bass, Kusuoka, Zhou and Kigami there is a well-established, rigorous mathematical framework for discussing such problems.The conference will contribute to the study of processes in disordered media (fractals), which have many applications in physics, chemistry, biological sciences and engineering. Diffusion processes in percolation clusters, vibrations of fractal objects, signal propagation in channels with random obstacles, electro-magnetic waves in fractal antennae, Rossby waves in oceanography, models of financial markets, neural structures are just a few of many examples of such processes. There are many important scientific questions involving modeling physical systems on fractal spaces. Participation of theoretical physicists helps foster the growing interactions between the mathematics and physics communities with interests in these areas. This conference will help inform the physics community of the infrastructure being developed by mathematicians, and will give mathematicians interesting feedback on the interests and questions of other scientists. These Cornell conferences have been held every three years starting in 2002. The previous four conferences in this series have had a major impact in the development of these areas by bringing together leading contributors, young researchers and mathematicians in related disciplines to learn about recent work and plan joint projects. The fifth conference is expected to continue in this tradition. The five day meeting will be structured in three parts: half-hour talks in the mornings by leading researchers in the field to describe recent important advances; mini-courses in the early afternoons to enable advanced undergraduates, graduate students, and researchers from related fields to learn some of the foundations of the area and discuss important open problems; and twenty minute talks in parallel sessions in the late afternoons to allow all attendees to present their research. A significant part of the conference is the mini-courses, which are directed primarily at the training of future mathematicians. A large number of junior researchers, including minorities, members of underrepresented groups and undergraduate students from both the Cornell and University of Connecticut REU programs, are expected to benefit from these courses.