Ines Adouani (Université de Sousse)
Title: Manifold-Based Transfer Learning: Efficient Techniques and Geometric Insights

Abstract: we consider the intersection of three research fields: transfer learning, statistics on manifolds, and information geometry. In particular, we propose a new efficient transfer learning approach for statistical models on the space of probability measures, denoted P. To this end, we first introduce the manifold structure on P equipped with the Fisher-Rao metric and the Levi-Civita connection. Using a local coordinate system, we introduce the Christoffel symbols, the geodesic, the exponential map, the logarithmic map, and the parallel transport. We then demonstrate that capturing such geometry yields significant benefits in the transfer learning of statistical models. Specifically, we propose a transfer learning method using the explicit expression of parallel transport. We show different applications where transferring a learned statistical model is of interest: Principal Component Analysis (PCA) and Linear Regression. The results prove the effectiveness of the proposed methods, with potential extensions to different real-world problems.  

Leila Ben Abdelghani (Faculté des Sciences de Monastir)
Title: Some recent results about the $SL(n)$-character variety of knot groups

Abstract: Many geometric and topological properties of a 3-manifold  M are encoded in the SL(2,C)-character variety . In recent years, there has been growing interest in the character variety of a  3-manifold   in other Lie groups, notably SL(n,C) pour n>2. A generalization of the work of Thurston and Culler-Shalen puts this area at the forefront of research in this field. In this talk, I will present some results on the SL(n,C)-character variety of a knot group that we have recently obtained in joint work with Michael Heusener.

Ali Baklouti (Faculté des Sciences de Sfax)
Title: Toward the resolution of the Zariski closure conjecture for exponential Lie groups.

Abstract: I will first define the Zariski Closure Conjecture of coadjoint orbits of exponential solvable Lie groups, and discuss the difficulties still rising toward its resolution. I will then propose new ideas on seeking the relationship between primitive ideals and coadjoint orbits and a solution to the conjecture.

Mehdi Lejmi (City University of New York, USA)
Title: Generalized almost-Kähler solitons

Abstract: In this talk, we discuss obstructions to the existence of Chern-Einstein metrics in the almost-Kähler setting. For instance, we introduce the notion of generalized almost-Kähler solitons and we disucss the exsitence and deformations of such metrics. This is a joint work with M. Albanese and G. Barbaro.

Mohamed Moakher (Pittsburgh, USA)
Title: Lois déterminants symplectiquesA

Abstract: La notion de pseudoreprésentations a été initialement introduite dans le cadre des les algèbres de groupes par Wiles (pour GL_2) et par Taylor (pour GL_d) dans le but de construire des représentations galoisiennes associées à certaines formes automorphes. Chenevier a proposé une théorie alternative des "lois déterminant" qui étend la définition de Wiles et Taylor à des algèbres arbitraires. Cette théorie s'est avérée utile dans l'étude des congruences entre les formes automorphes et dans la théorie de la déformation des représentations galoisiennes résiduellement réductibles. Dans cet exposé, je vais présenter mon travail en collaboration avec Julian Quast sur les "lois déterminant symplectiques", qui adapte le cadre de Chenevier au groupe symplectique GSp_2d. Je donnerai la définition et certaines de ses propriétés clés, puis expliquerai sa relation avec la Théorie Géométrique des Invariants (GIT) et les Variété des caractères.

Antonio Rieser (CONACYT - CIMAT Guanajuato, Mexico)
Title: Homotopy and homology for graphs an data through pseudo topological and closure spaces

Programme :

Thursday 18 juillet 2024

8h30-9h10 Accueil des participants.

9h10-10h00 Antonio Rieser

10h-10h20 Pause-café.

10h30-11h20 Leila Ben Abdelghani

11h30-12h20 Mehdi Lejmi

Lunch.

14h00-14h50 Mohamed Moakher

15h00-15h50 Ines Adouani

16h00-16h20 Pause-café.

16h30-17h20 Ali Baklouti.