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

Cornell University, Ithaca NY

Investigators

Abstract

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.