BSI Forum: Information Geometry from the Perspective of Affine Differential Geometry

January 29-30, 2006
Laboratory of Mathematical Neuroscience
RIKEN BSI
(BSI Center Building 2F S205)

Organizers: Jun Zhang (University of Michigan) Hiroshi Matsuzoe (Nagoya Institute of Technology)

Affine differential geometry studies hypersurfaces immersed into an affine ambient space and the induced geometrical structure. A key fact is that dual connections arise naturally through considering the component of covariant derivatives which is tangent to a pair of dually constructed hypersurfaces. Recently, considerable progress has been made towards modeling statistical manifolds as affine immersions of hypersurfaces with codimension(s) one and two. Since the resulting dualistic structure does not require a priori the existence of a metric on the ambient space, this approach may elucidate some fundamental issues in classical information geometry, and generate significant insight in the geometric relations (e.g., conformal, conformal-projective, and projective) among various statistical (sub)manifolds.

This one-and-a-half day forum will review basic concepts of affine differential geometry, survey the current results in hypersurface realization of statistical manifolds, and define open problems, in both theory and application, that can be tackled by formulating them as problems in affine hypersurface theory.

The unique feature of this forum is that it is technically oriented - it provides hands-on tutorials to computations and derivations by allowing interruptions to presentations and group discussions with open exchange.

Attendance of the forum is free and open to any interested party. However, in order to make logistic, participants are required to register before January 20, 2006, by sending an email to the organizer: m a t s u z o e atmark n i t e c h dot a c dot j p (The organizers would appreciate if you inform us your research field, for example, geometry, statistics, etc.) The forum will be conducted (in most part) in English.

PROGRAM

Copyright (C) 2005- Matsuzoe Hiroshi