General Information

The French-Russian Poncelet Laboratory organizes the conference on "Random Processes, Conformal Field Theory and Integrable Systems", September 19-23, 2011, to take place in the Independent University of Moscow.

Random processes have an impressive number of applications that range from mathematics, physics, chemistry, biology to subjects such as computer science and finance. In the last decades, the understanding of these processes has greatly benefited from the use of conformal field theory (CFT) and integrable systems (IS) which have been widely studied in the community of theoretical and mathematical physicists. For instance, the geometrical characterization of 2D polymers has been shown to be related to the data characterizing a given CFT. During the last years, new and amazing connections between random processes and CFT/IS approaches have been discovered. The most known is the connection between stochastic Loewner evolution (SLE) and CFT which, besides providing a new perspective for studying critical systems, has produced many spectacular results concerning Brownian motion, percolation models and self-avoiding walks. In the last months, new relations have been established between vicious random walks and directed polymer in random media on one hand, and well known integrable models on the other hand. These connections have paved the way for a better understanding of these systems which are at the heart of many applications in statistical physics.

At the same time, new aspects of random processes and their applications in biology have been recently discovered. Among the others, one can mention intermittent random processes with two alternating "phases" of motion (e.g., passive diffusion and active ballistic transport in living cells). These processes are believed to be responsible for main biochemical reactions in living cells, including searching for specific DNA sites by proteins. Although each "phase" of motion may be quite well understood, deterministic or random switching between them lead to new, often unexpected results. For instance, an intermittent search mechanism in simple spherical domains has been shown to be more efficient than either of the constitutive motions. But the optimality of the intermittent search remains an open question for complex domains, by the lack of appropriate mathematical tools. The use of powerful methods of CFT/IS can significantly advance this field with numerous far-reaching applications in biology.

The proposed workshop is a 5 days-long progra dedicated random processes, conformal field theory and integrable systems. Each day will start with a one-hour survey lecture to provide a pedagogical introduction to the topic for the participants from the other fields. Five talks presenting recent original research by the leading experts will then be given, each of them followed by informal discussions. Particular attention will be paid to the interactions between these three fields. In the evening we plan to organize panel discussions on the cross-disciplinary problems and future developments in the field.

In order to attract promising students and young researchers, a topical school will be organized in Saint Petersburg (14-17 September 2011).