# Calendar

## December 2022

### Robustness of active anisotropic deformation in developing biological tissues.

Soutenance de thèse de Muhamet Ibrahimi (directrice de thèse E. Floriani, co-directeur M. Merkel)

### Universal entropy estimators (attention horaire inhabituel)

#### Vojkan Jaksic (Université de McGIll)

The performance studies of the celebrated Lempel–Ziv coding algorithm have led to some deep insights into the specific entropy and relative entropy of stationary measures on shift spaces.

Notable among those is the characterisation of the specific entropy of a stochastic source in terms of the exponential asymptotics of recurrence times of a typical signal, and the related characterisation of the specific cross entropy in terms of waiting times. These and other related entropic estimators

have found diverse practical applications beyond information theory.

In this talk I will describe a research program dealing with refinements of the mathematical theory

of entropic estimators that originated in information theory, and to their theoretical and practical

applications.

Based on the joint works with G. Cristadoro, M. Degli Esposti, and R. Raquepas.

https://arxiv.org/pdf/2209.09716.pdf

https://arxiv.org/pdf/2209.09717.pdf

### Thesis defense: Noncommutative Geometry and Gauge theories on 𝐴𝐹 algebras

#### Gaston Nieuviarts

Non-commutative geometry (NCG) is a mathematical discipline developed in the 1990s by Alain Connes.

It is presented as a new generalization of usual geometry, both encompassing and going beyond the Riemannian

framework, within a purely algebraic formalism. Like Riemannian geometry, NCG also has links with

physics. Indeed, NCG provided a powerful framework for the reformulation of the Standard Model of Particle

Physics (SMPP), taking into account general relativity, in a single "geometric" representation, based on Non-

Commutative Gauge Theories (NCGFT). Moreover, this accomplishment provides a convenient framework to

study various possibilities to go beyond the SMPP, such as Grand Unified Theories (GUTs). This thesis intends to

show an elegant method recently developed by Thierry Masson and myself, which proposes a general scheme to

elaborate GUTs in the framework of NCGFTs. This concerns the study of NCGFTs based on approximately finite

𝐶∗-algebras (AF-algebras), using either derivations of the algebra or spectral triples to build up the underlying

differential structure of the Gauge theory. The inductive sequence defining the AF-algebra is used to allow the

construction of a sequence of NCGFTs of Yang-Mills Higgs types, so that the rank 𝑛 + 1 can represent a grand

unified theory of the rank 𝑛.The main advantage of this framework is that it controls, using appropriate conditions,

the interaction of the degrees of freedom along the inductive sequence on the AF algebra. This suggests

a way to obtain GUT-like models while offering many directions of theoretical investigation to go beyond the

SMPP.

### Développements récents en difféologie

#### Patrick Iglesias-Zemmour (The Hebrew University of Jerusalem, Israel)

Je parlerai des récents développements en difféologie du point de vue mathématique mais aussi ayant un rapport avec la physique théorique, en espérant susciter la curiosité et des questions nouvelles.