Topics in Applied Nonlinear Analysis: Recent Advances and New Trends

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This award will provide support for participants of the conference on "Topics in Applied Nonlinear Analysis: Recent Advances and New Trends," to be held at the Center for Nonlinear Analysis (CNA) at Carnegie Mellon University, Pittsburgh, in July 18-20, 2016. The conference will be devoted to the topics of applied analysis that in many ways revolutionized the field, especially for our understanding of behavior of materials and design of materials with desired properties. These areas are of critical importance to maintaining US leadership in science and technology as evidenced, for instance, by the recently launched, multi-agency Materials Genome Initiative. The conference will continue the CNA tradition of offering extraordinary networking and training opportunities for students and junior researchers to interact with a remarkable group of leading national and international researchers in applied analysis. This conference will provide an exceptional venue for top researchers in applied mathematics and in materials science to interact and share recent advances with a diverse audience. The impact of the conference is expected in both the mathematical and engineering communities. Detailed plans have been made to help recruit a diverse group of participants from the scientific community, including women and minorities. Scientific and social activities will be organized to give young trainees exposure and promote their excellence. These include a poster session with awards for four best posters, identified by a group of judges selected from top experts in both fields. The results of the conference will be disseminated by means of a dedicated website featuring video recordings of all invited presentations: https://www.math.cmu.edu/CNA/kinderlehrer75/index.html This conference will bring under one umbrella contemporary trends in nonlinear analysis, emphasizing two scientific areas where the interplay between the classical and the modern, the theoretical and the applied in analysis has been especially prominent: (1) Optimal Transport and (2) Mathematics of Materials. Among others, the topics will include: - Recent advances in variational inequalities, non-convex variational problems, Gamma-convergence and optimal transport;- Applications to PDE;- Modeling and Analysis of Problems in Materials Science: materials microstructure and design of smart materials;- Computational Methods with Application to Problems in Materials Science and Mathematical Biology: recent developments in Finite Element Methods, Virtual Element Methods and Quasi-Continuum Methods.New collaborations that are likely to emerge from this activity will have a potential to catalyze research at the interface between theoretical/applied partial differential equations and various engineering disciplines, and will result in cross-pollination of ideas.