This award provides funding to help defray the travel expenses of 18 US participants, especially young researchers and graduate students, to participate in the conference "Beyond Hamilton-Jacobi in Avignon", which will take place in Avignon University, from Wednesday April 23 - 30, 2014. The PIs expect that about 2/3 of the budget will go towards the support of graduate students and postdocs, with recruiting as many underrepresented groups as possible a priority.
The Avignon conference will cover recent developments in the areas of Weak KAM theory and Aubry-Mather theory. This is a very active area, with origins in practical applications to solid state physics and dynamics. The Avignon conference will bring together participants from many parts of the world to enrich and connect the many different aspects of Weak KAM theory. The junior researchers from the US will be exposed to a high level program and will become acquainted with the most promising and vibrant areas of research connecting PDEs to dynamics. There will be 6 senior lecturers, including the two PIs who are also co-organizers of the event.
The goals of this project was contribute to fund the attendance of USA participants (mainly junior participants) for a conference in Avignon. The main funding from the conference came from outside of the USA. The main goal of the conference was to review the rapid progress t in the last years in the so-called Hamilton Jacobi equations. These are some Partial differential equations which have appered in many different areas. They originally appeared in Optics (as a description of the optical phase). Immediately they found applications in mechanics and geometry and, more recently in economics and in stochastic control. The main reason Hamilton-Jacobi equations appear is that many processes involve optimization. If one changes the conditions, the optimizer has to change. Hamilton-Jacobi equations describe this change on the optimal solution with respect to the boundary conditions. They are rather subtle because even if they are differential equations, the solutions may present singularities. Even if the subject is centuries old, there has been explosive progress when it was realized about 20 years ago that sophisticated PDE methods could interact with methods from dynamics and geometry. The conference aimed also to include other aspects that go beyond the traditional topics. For example, stochastic aspects, relations with convexity, mean field games, etc. As indicated in the title, the main goal was to expand the scope. The conferece feautured many of the main players in the topic and provided the specialists a way to present the results and to learn of the main novelties. There were tutorial aspects for the young researchers to get an entry point in the field. Having this up to date introduction and having the opportunity to develop international contacts will be a very valuable asset for the career of the junior participants. Many of them got good ideas of possible directions of research and some of the technical tools and contacts.
