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

康奈尔大学第五届分形分析、概率和数学物理会议

• 批准号: 1361934
• 负责人: Robert Strichartz
• 金额: $ 4.95万
• 依托单位: Cornell University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-04-01 至 2015-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1361934&HistoricalAwards=false
• 关键词: Cornell; Fifth; Conference; Analysis; Probability

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.

第五届分形分析、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。分形在当前数学研究中出现的方式有很多。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类似物，随机过程和发生在这些分形空间上的物理相互作用模型。由于Barlow， Perkins, Bass, Kusuoka， Zhou和Kigami的开创性工作，有一个完善的，严格的数学框架来讨论这些问题。会议将有助于研究无序介质（分形）中的过程，这些过程在物理、化学、生物科学和工程中有许多应用。渗透簇中的扩散过程，分形物体的振动，随机障碍物通道中的信号传播，分形天线中的电磁波，海洋学中的罗斯比波，金融市场模型，神经结构只是此类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社区之间日益增长的互动。这次会议将帮助物理界了解数学家正在开发的基础设施，并将为数学家提供关于其他科学家的兴趣和问题的有趣反馈。这些会议从2002年开始每三年举行一次。该系列的前四次会议对这些领域的发展产生了重大影响，汇集了相关学科的主要贡献者、年轻研究人员和数学家，了解最新的工作并计划联合项目。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，介绍最近的重要进展；下午早些时候的迷你课程，使来自相关领域的高级本科生、研究生和研究人员能够学习该领域的一些基础知识，并讨论重要的开放性问题；在下午晚些时候的平行会议上进行20分钟的演讲，让所有与会者展示他们的研究。会议的一个重要部分是小型课程，主要是针对培养未来的数学家。大量的初级研究人员，包括少数民族，代表性不足的群体成员以及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。