Recent progress on nonlinear elliptic and parabolic problems and related abstract methods (07w5004)

Objectives

The main purpose of this workshop is to bring together international leaders and active researchers working on a selection of areas in nonlinear elliptic and parabolic problems and related abstract methods, where significant recent progress is being made, to exchange new ideas and results, and to further progress research in these areas through new collaboration and cross-fertilization.

Topics to be covered by the workshop will include elliptic and parabolic problems arising from mathematical biology, chemical reaction theory, material science and water waves, and related abstract methods. Special emphasize will be put on the analysis of a number of important features of these problems, such as spatial and temporal patterns (Berestycki, Cosner, Lou, Mischaikow, Matano, etc.), sharp layers and spikes (Bates, Dancer, Del Pino, Felmer, Gui, Ni, Yan, Wei, etc.), blow-up (Matano, Polacik, etc.), traveling waves (Berestycki, Matano, Yanagida, etc.), and some of the techniques involved in these problems, including topological and variational methods (Bartsch, Dancer, Ghoussoub, Mawhin, Mischaikow, Rabinowitz, Schmitt, etc.), bifurcation theory (Dancer, Du, Schmitt, Toland, etc.) , singular perturbation (Aftalion, Alama, Dancer, Gui, Ni, Yan, Ward, Wei, etc.), infinite dimensional dynamical systems (Bates, Matano, Mischaikow, Polacik, Quittner, Shen, Yanagida, Zhao, etc.), elliptic and parabolic estimates (Berestycki, Ghoussoub, Li, Peletier, Stuart, etc.).

In view of the rapid progress made in recent years in the study of these problems, and the geographic diversity of the researchers in this field, it is timely and important to bring a carefully selected group of experts to a 5-day workshop to facilitate the dissemination of the most recent research ideas and techniques. It is highly hoped that the atmosphere of the workshop and its surroundings will lead to new collaborations during and especially in the years following the workshop. Interaction of these related but different areas has proven crucial in groundbreaking recent research; for instance,
analytic bifurcation theory was instrumental in solving an old problem of Levi-Civita on water waves recently, and some old questions on multiplicity of solutions in variational problems have been solved by recent singular perturbation techniques in the study of peak solutions.

The list of proposed participants includes a good mixture of both some of the most distinguished mathematicians in the world and many of the top young researchers in the field. To encourage interaction, we plan to ask participants to send the organizers abstracts of their talks, and bring recent papers for distribution during the workshop.