The aim of the conference is to bring together researchers in a range of fields within stochastic analysis from all over the world, to survey recent developments, exchange ideas and to foster future collaborations. The main topics include stochastic partial differential equations, measure valued processes, random walks in random media, Dirichlet forms and diffusions on fractals. We will focus on the common theme of developing new foundational methods which will be useful to various areas within stochastic analysis as well as to problems motivated by
This talk has two parts. The common themes are the very interesting properties of flag domains and their quotients by discrete subgroups present only in the non-classical case.
The first part will give a general overview of these properties, especially as they relate to several of the other talks being presented at this conference.
The second part will focus on one particular property in the non-classical case. When suitably localized, the Harish-Chandra modules associated to discrete series -- especially the non-holomorphic and totally degenerate limits (TDLDS) of such -- may be canonically realized as the solution space to a holomorphic, linear PDE system. The invariants of the PDE system then relate to properties of the Harish-Chandra module: e.g., its tableau gives the K-type. Conversely, the representation theory, especially in the case of TDLDS, suggest interesting new issues in linear PDE theory.