These conferences are intended to stimulate interest and activity in mathematical research. Each five day conference features a distinguished lecturer or team of lecturers delivering ten lectures on a topic of important current research in one sharply focused area of the mathematical sciences.
The lecturer or lecturers prepare extensive online materials that are made available at https://www.cbmsweb.org/regional-conferences/past-conferences/. They are also expected to prepare an expository monograph based upon these lectures, which is normally published as a part of a regional conference series.
Depending upon the conference topic, the monograph is published by the American Mathematical Society, the Society for Industrial and Applied Mathematics, or jointly by the American Statistical Association and the Institute of Mathematical Statistics.
Support for about 30 participants is provided and the conference organizer invites both established researchers and interested newcomers, including postdoctoral fellows and graduate students, to attend. Information about an individual conference may be obtained by contacting the conference organizer.
This conference will focus on the most recent developments in mathematical methods for optical metamaterials. Topics include:
The goals of this conference include:
(i) presentation of the state-of-the-art mathematical research in subwavelength metamaterials and new developments in material sciences for graduate students and postdoctoral and junior researchers from applied mathematics, physics and engineering.
(ii) charting future directions and formulating open problems in this interdisciplinary field; and, (iii) establishing new collaborations across the boundaries of mathematics, physics and engineering.
(iii) establishing new collaborations across the boundaries of mathematics, physics and engineering.
Algorithmic fractal dimensions were first developed at the beginning of this century as measures of the density of information in various mathematical objects. As the name suggests, they are versions of classical fractal dimensions that have the theory of computing embedded in their definitions. They have already had applications in computability theory, computational complexity, information theory, and number theory. Most strikingly, algorithmic fractal dimensions are being used with increasing frequency to prove new theorems–some answering long-standing open problems–in classical fractal geometry, theorems whose statements do not involve computability or related aspects of mathematical logic. The lectures will provide an introduction to the various notions of algorithmic fractal dimension and their applications to areas such as geometric measure theory, computational complexity, information theory, and the theory of Borel normal numbers. Beyond the lectures, the conference will provide ample time for open problem sessions and other discussions. The conference will thus be of interest to participants from multiple research communities; outreach for conference participation will reflect this breadth and will prioritize early-career researchers, members of historically underrepresented groups, and a range of institutions in the Midwest.
Inverse problems, which are interdisciplinary in nature, occur in the mathematical modeling of real-world applications where direct observations of certain properties are not possible.
While there has been much important work on inverse problems over the last few decades, most of these efforts have focused on linear PDEs or PDE systems. Contrary to the common belief that the presence of nonlinearity is an obstacle, a recent major breakthrough has shown that nonlinearity can actually be used as a tool to solve inverse problems. The series of lectures at this conference will show in detail how nonlinearity can help in a variety of inverse problems arising in nonlinear wave propagation, nonlinear analogs of Calderon’s inverse problems, nonlinear transport equations, and inverse scattering for nonlinear PDEs. The lectures along with other activities will afford opportunities for the conference participants, especially graduate students and young researchers, to discuss fundamental ideas and open problems. The regional emphasis of this conference also will strengthen the collaborations among researchers working in inverse problems
and related fields in the southeast, as well as establish new research programs.