The main plan is to have activities spanning frontier topics of research in Discrete Mathematics (including Combinatorics and Optimization) and Probability during the year. In the Fall term, the focus will be on probabilistic, extremal, geometric, and enumerative aspects of Combinatorics, and convex and other nonlinear programming aspects of Optimization, while during the Spring term, the focus will more on information theoretic, geometric and functional analytical aspects of Probability and Analysis. Both will touch upon and address applications to various other disciplines. Concentration of measure phenomenon and isoperimetry have played a major inspirational role in the development of new theories as well as analytical techniques in both the discrete and the continuous setting of probability. Application areas range from the Hardness of Approximation Algorithms in Computer Science to Mass Transportation Theory in PDE and Analysis. Several geometric, functional and isoperimetric inequalities classically developed in discrete and continuous settings can now be placed on a common framework (thanks to the efforts of many experts, identified in the list of visitors below, besides the recent Fields medalist Cedric Villani), while much needs to be further developed and better understood in the discrete settings of graphs and finite Markov chains. We hope the synergistic year will provide a great opportunity for the discrete and the continuous worlds to interact more frequently and fruitfully.

One of our specific goals will be to use this forum to make the state-of-the-art more accessible to a broader audience, in particular, planning of tutorial lectures, participation by graduate students of various mathematical backgrounds and postdoctoral researchers will be a priority. It would be of great benefit to gather leading researchers in these various sub-fields to facilitate exchange of knowledge, and also to identify new research directions so as to expand the horizons. We thus expect a thematic year of this nature to have a lasting impact on the future of the subject.