Schedule
Wednesday  
March 15 
 
Thursday  
March 16 
 
 

 
 

14h14h50  
H. ISHI 
 
9h009h50  
T. OHIRA 
15h15h30  
Y. ISOWAKI 
 
10h0010h50  
Ph. REGNAULT 
Pause café 
 
Pause café 
16h0016h50  
G. MENDOUSSE 
 
11h3012h20  
A. KEZIOU 
17h0017h30  
K. ARASHI 
 
 



Speakers
 K. Arashi (Nagoya University)
On SO*(n) and its representations.
The Lie group SO*(n) is an example of Hermitian Lie group. One of its
definition is given by SO*(n) = SO(2n, C) \cap M(n, H), where M(n,H)
is the set of quaternionic matrices realized as a subspace of M(2n,C).
We show that the determinant of any matrix in M(n,H) is positive,
which implies that SO*(n) coincides with O*(n) = O(2n, C) \cap
M(n,H). Moreover, we discuss holomorphic discrete series
representations of SO*(n).
 H. Ishi (Nagoya University/ JST PRESTO)
New class of convex
cones inspired by statistics
Symmetric cones are fascinating research objects attracting
mathematicians working on various areas including representation
theory and mathematical statistics. Thanks to their rich symmetry, we
have beautiful analytic formulas over the symmetric cones, and some of
the formulas are generalized to nonselfadjoint homogeneous cones. On
the other hand, statisticians found similar formulas for the cone of
positive definite symmetric matrices with prescribed zero components,
where the position of zeros are assigned by chordal graphs, despite
the lack of transitive group actions. In this talk, we present a new
class of convex cones consisting of real symmetric matrices with
specific block decomposition. The class contains both homogeneous
cones and the cones corresponding to chordal graphs, so that we get a
unified machinery to investigate the two types of cones.
 Y. Isowaki (Nagoya University)
Orbit method for some Lie groups.
The theory of orbit method is founded by A.A. Kirillov in 1962.
Kirillov's original orbit method claims the onetoone correspondence
between equivalence classes of irreducible unitary representations and
coadjoint orbits of connected and simply connected nilpotent Lie
group. Furthermore, it is known that this relation holds not only for
nilpotent Lie groups but also for some other classes of Lie groups.
In scheme of the orbit method, the notion of induced representation
plays a fundamental role. Actually, induced representation is a
universal method of constructing representations of a given group from
representations of its (closed) subgroup.
In this talk, we first introduce the notion of induced representation
from the view point of vector bundles. Then, we observe orbit method
for some simple examples.
 A. Keziou (Reims University)
Duality of divergences and its use in semiparametric statistics
We investigate the Fenchel duality theory, for the multivariate divergences between measures,
viewed as convex functionals on well chosen topological vector spaces of signed finite measures.
We give dual representations of these criteria,
which we use to define new family of estimates and test statistics, with multiple samples
under semiparametric density ratio models, extending the empirical likelihood method.
Moreover, we present how to use the estimated ratios, obtained through the above approach,
to define multigroup classifiers.
 G. Mendousse (Reims University)
Some aspects of harmonic analysis on quaternionic homogeneous spaces
We introduce specific representations of the Lie group G=Sp(n,C) (principal series) on the Hilbert space L^2(S^{4n1}). We study them by restricting to its maximal compact subgroup K=Sp(n) and obtain the list of invariant irreducible components (Ktypes) that add up to L^2(S^{4n1}). Elements of these components that satisfy some suitable invariance property can be associated to specific special functions. We explain how it works when one studies the orthogonal group O(4n) instead of the symplectic group Sp(n), we reestablish classical results and then generalise to Sp(n).
 T. Ohira (Nagoya University)
Delayed
stochastic systems
Noise and time delay are two elements that are associated with many natural systems, and often they are
sources of complex behaviors. Understanding of this complexity is yet to be explored, particularly when both
elements are present. we investigate such delayed stochastic systems both in dynamical and probabilistic perspectives: Langevin
equation with delay and a randomwalk model whose transition probability depends on a fixed timeinterval
past, called Delayed Random Walks. A peculiar resonance behavior with noise and delay, called ?Delayed Stochastic Resonance?
will be also discussed. We present some examples of applications of these delayed stochastic systems.
 Ph. Regnault (Reims University)
Statistical inference based on divergence minimization and information geometry.
Since the early developments of statistical mathematics, divergences between probability measures have played a prominent role, as they measure the dissimilarity from observations to some expected behavior. In the context of parametric statistics, classical divergences such as KullbackLeibler or CressiRead divergences induce a Riemannian geometric structure on the model under study. Classical results  and some others  in statistics for independent samples can be derived through the study of this geometry, referred to as information geometry.
In the first part of the talk, we will illustrate some of these informational geometric properties through its application to a large deviations principle for a sequence of estimators of Shannon entropy of a distribution, based on independent observations drawn according to this distribution.
Very little attention has been devoted in the literature to informational geometric properties of divergence between Markov chains. As a first attempt to go further in that direction, we will establish in a second time, closed form expressions for divergences between Markov chains.
