Annales de la Faculté des Sciences de Toulouse

K. D. Elworthy

I. Gentil

M. Ledoux

F. Malrieu

B. Zegarlinski

ANNALES
DE LA FACULTÉ
DES SCIENCES
Mathématiques
K. D. ELWORTHY, I. GENTIL, M. LEDOUX,
F. MALRIEU AND B. ZEGARLINSKI
Preface
Tome XXVI, no 2 (2017), p. i-i.
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Preface
It is a priviledge to preface this issue of the Annales de la Faculté des
Sciences de Toulouse in honour of Dominique Bakry. In December 2014, an
international conference was held in Toulouse on the occasion of his 60th
birthday. The articles gathered here at this occasion are a tribute of the
authors to Dominique Bakry, covering a wide field of interests around the
ideas that he set in motion and continues to develop. We thank them all for
their contributions. We also thank the editorial board of the Annales de la
Faculté des Sciences de Toulouse, and in particular its chief-editor J.-P. Otal,
for the very efficient handling of the submissions.
After a CNRS position in Strasbourg, Dominique Bakry became Professor
at the University of Toulouse, Paul-Sabatier, in 1988. His Phd thesis, under
the joint supervision of M. Yor and P.-A. Meyer, was devoted to the gen-
eral theory of multi-parameter processes. He then explored Riesz transforms
and emphasized a new analytic and geometric theory of Markov diffusion
operators. This theory, in which he introduced the famous Γ2 operator and
the fundamental notion of curvature-dimension of a Markov generator, has
developed into a very fruitful and active research area in which the curva-
ture criteria are cornerstones of deep interaction within analysis, geometry
and probability theory. The field was even further enhanced during the last
decade in connection with the synthetic curvature of optimal transport of
J. Lott, C. Villani and K.-T. Sturm. More recently, Dominique Bakry opened
a new research programme on the diagonalization of multi-dimensional diffu-
sion operators in bases of orthogonal polynomials, yielding striking new con-
nections between the functional calculus associated to the carré du champ
operator and algebraic geometry. This line of research illustrates his con-
stant dynamic search for new fields of mathematics and for bridges between
different concepts.
The current rich activities on the analysis and geometry of diffusion op-
erators and their applications, in particular illustrated in this volume, un-
derline the importance and the relevance of the concepts and principles put
forward by Dominique Bakry. We are most happy to dedicate these lines to
Dominique Bakry, as a tribute to his achievements, past and future.
K. D. Elworthy, I. Gentil, M. Ledoux, F. Malrieu, B. Zegarlinski
– i –


Preface

Pascal Remy

Resurgence and highest level’s connection-to-Stokes formulæ for some linear meromorphic differential systems

Oren Ben-Bassat

Kobi Kremnizer

Non-Archimedean analytic geometry as relative algebraic geometry

Christophe Sabot

Laurent Tournier

Random walks in Dirichlet environment: an overview

Ivan Gentil

Christian Léonard

Luigia Ripani

About the analogy between optimal transport and minimal entropy

Delphine Moussard

Equivariant triple intersections

Joscha Diehl

Peter K. Friz

Wilhelm Stannat

Stochastic partial differential equations: a rough paths view on weak solutions via Feynman–Kac

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Preface

Resurgence and highest level’s connection-to-Stokes formulæ for some linear meromorphic differential systems

Non-Archimedean analytic geometry as relative algebraic geometry

Random walks in Dirichlet environment: an overview

About the analogy between optimal transport and minimal entropy

Equivariant triple intersections

Stochastic partial differential equations: a rough paths view on weak solutions via Feynman–Kac

Harmonic Measures on the Sphere via Curvature-Dimension

Unbounded rough drivers

Geometric diffusions of 1-currents

1,744

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