Lectures on Probability and Stochastic Processes XI
The eleventh meeting of the Lectures on Probability and Stochastic Processes will be held at the Indian Statistical Institute, Delhi Centre, during November 25 - 29, 2016. The lectures will be held in the Auditorium. Information on how to reach I.S.I. can be obtained by following the link http://www.isid.ac.in/reaching_isid.html.
The topics are the following.
The past few years have been witness to a resurgence of tremendous interest in the field of stochastic partial differential equations [SPDEs, for short]. This is, in part because of the intrinsic mathematical elegance of the subject matter, and in part due to its various connections to a large number of applied scientific problems of current interest.
This 8-lecture-long course begins with an introduction to parabolic stochastic partial differential equations, and then proceeds to study the structure, as well as the behavior, of the solution in several physically-interesting cases. Familiarity with Itô calculus will be assumed.
While convexity of sets and functions on linear spaces is bread-and-butter to any mathematician, the notion of convexity for measures - although deeply studied by Christer Borell starting in the 1970's - is far less well known. The goal of these lectures will be to provide an exposition as well as motivation for the theory of convex measures, focusing in particular on the important and ubiquitous subclass of log-concave measures. The lectures will choose an eclectic path through some of the many aspects of the theory that have been developed in the last 40 years, covering some classical topics (such as the Prékopa-Leindler inequality), some developed around the turn of the millennium (such as transportation inequalities and connections to the concentration of measure phenomenon), and some very recent topics (such as Klartag's central limit theorem and the concentration of information content). We also hope to discuss (although sketchily and in passing) some applications of the theory, including to random matrix theory, stochastic simulation, optimization, and statistical physics.
Note: LPS XII will be held in Indian Statistical Institute, Kolkata during December 15th - 19th, 2017. The speakers for the same are the following.