COMPLEX DYNAMICS AND APPLICATIONS
COMPLEX DYNAMICS AND APPLICATIONS
Course description
An introduction to complex dynamics, aimed to survey its recent applications to statistical mechanics and the related open problems. A good portion of this course will be dedicated to review the classical theory of dynamics in one complex variables, initiated by Fatou and Julia. The emphasis will be on the ideas and results used in the recent progress in statistical mechanics; specifically, on the zeros of the partition function of the hard-core gas model (Peters–Regts, Bezakova–Galanis–Goldberg–Stefankovic). The course will end with a discussion of open problems.
Course description
An introduction to complex dynamics, aimed to survey its recent applications to statistical mechanics and the related open problems. A good portion of this course will be dedicated to review the classical theory of dynamics in one complex variables, initiated by Fatou and Julia. The emphasis will be on the ideas and results used in the recent progress in statistical mechanics; specifically, on the zeros of the partition function of the hard-core gas model (Peters–Regts, Bezakova–Galanis–Goldberg–Stefankovic). The course will end with a discussion of open problems.
Lecturers
Email: jriveral@ur.rochester.edu
Juan Rivera-Letelier (University of Rochester)
Biosketch
Juan Rivera-Letelier is a Professor of Mathematics at the Rochester University, USA. Previously, he was in Pontificia Universidad Católica, in Santiago (Chile). He has held positions al Brown University, where he was a distinguished visiting associate professor, and at the Institute for Mathematical Sciences at SUNY Stony Brook, where he was a postdoctoral researcher. He obtained his PhD at the Université de Paris Sud in 2000.
Rivera-Letelier’s research is primarily in the area of dynamical systems, which can be described as the theory of long-term behaviour of maps under iteration. The main focus of his research has been on one-dimensional systems of diverse origin: arithmetic, p-adic, real, and complex. He has recently applied ideas from dynamical systems to the study of statistical mechanics, in particular, the area of low temperature phase transitions.
Find a long interview with him (in Spanish) here.
References
John Milnor, Dynamics in one complex variable.
Barry Simon, The statistical mechanics on lattice gases