Mathematics and Mechanics in the 22nd Century: Seven Decades and Counting...

This grant provides partial support for a conference on 'Mathematics and Mechanics in the 22nd Century: Seven Decades and Counting...' to be held October 23-25, 2015, in Eugene, Oregon. The interaction between mathematics and mechanics, with ensuing applications to materials science and biology, will be the central theme of the conference. The grant will support travel expenses of young scientists to participate in the conference and present a poster in the blitz and exhibit sessions. The late 1940s saw the beginning of new trends in the development of a continuum theory of complex materials and the foundation of theories that bridge continuum mechanics and molecular and atomic structure. These new areas of inquiry were catalytic to the development of new mathematical and mechanics theories at the basis of design of new materials and devices, with applications from medicine to advanced manufacturing. The conference has two main goals. First, it will explore recent developments and new trends and will identify prospects for future research on nonlinear materials, devices, biological modeling, and related mathematical and computational ideas and tools. The interdisciplinary school of scientists at the forefront of such developments during the last seven decades has mentored and produced new generations of outstanding scientists, which include a large number of women, who have themselves reached leadership roles in the field. Thus, another main goal of the conference is to discuss mentoring strategies for future generations to ensure the continued scientific and human development success and to reach out to members of underrepresented groups. The participants will explore tools to overcome the challenges of an incipient career in interdisciplinary research and identify new educational demands. Another organizational task will be identifying an academically diverse pool of junior researchers across the USA and oversees, with a very strong presence of women and members of underrepresented groups.

Nonlinear elasticity emerged in the mathematical community as a result of the works by Ericksen and Rivlin, from the late 1940s to 1960s. This initiated a golden period of research in the calculus of variations and partial differential equations, from the points of view of both analysis and geometry. These developments also lead to outstanding success in the field of complex materials, such as the theories of phase transformations in crystals, shape memory alloys, ferroelectric and magnetic materials, composites, and liquid crystals. While the selection of conference speakers is made in connection with these themes of research, the emphasis will be placed on new and prospective mathematical and materials developments and applications. These will include topics on materials research leading to new sources of clean energy, as well as new mathematical tools to understand and compute defects in liquid crystals and ensuing applications to electrolytic transport, and mechanical studies of viruses towards research on antibiotic-resistant bacteria. The conference also envisions a scientific panel on strategies for new materials development, accompanying mathematical tools, and interdisciplinary and educational challenges. The website for the conference can be found at http://www.ima.umn.edu/2015-2016/SW10.23-25.15/