Geometry AND Arithmetic
Geometry AND Arithmetic
---------------
The Ph. D defense of RAZAFINJATOVO Mahefason Heriniaina which will take place on Tuesday 17th of May 2022 from 9 AM to 10 AM. at the University of Antananarivo (Salle des thèse).
Zoom link:
https://us04web.zoom.us/j/73196437088?pwd=pI9Z0Pfml5eUW83opHRaSI6HC5ZvFf.1
Password: ganda
Title: Bornes sur les coefficients des Polynômes modulaires de Drinfeld (Ph. D in french)
Jury members:
Randriambololondmanalala Princy, University of Antananarivo, Edma.
Randrianarivony Arthur, University of Antananarivo, Edma.
Rabarison Patrick, University of Antananarivo.
Rück Hans-Georg, University of Cassel, Germany.
Razafimanatssoa Gerard, University of Antananarivo, Edma
Scientific Director: Mr. Rajoelina Michel Martin, University of Antananarivo, Edma.
co- Scientific Director: Breuer Florian
See here for the course notes and gp scripts : https://webusers.imj-prg.fr/~pascal.molin/cours/tana2019/
Stéphane LAUNOIS, Kent University ''Algèbres de Poisson et plus"
Samuel LOPES, University of Porto: ''From symmetry to non-associativity and back"
Pasha ZUSMANOVICH, d'Ostrava University ''Introduction to cohomology algebras"
Date: Mardi 9 Avril 2019 à 15 heures
Intervenant: Hery Randriamaro
Salle: Bibliothèque des Mathématiques
Abstract: The concept of coloring originates from the map coloring problem. Visualize a map of the six regions of Madagascar: Antananarivo, Antsiranana, Fianarantsoa, Mahajanga, Toamasina, and Toliara. We assign a vertex to each region, and connect two vertices only when the corresponding regions have a common border. In this way, a graph is assigned to any map of territories. Its dual graph is formed by each vertex from each face, Antananarivo--Fianarantsoa--Toamasina forms a face for example, a last vertex outside Madagascar, and the dual edges joining these vertices. A graph coloring corresponds to a way of coloring the map so that two connected territories are differently colored. In 1954, Tutte built a polynomial in two variables that can enumerate the colorings of a graph and of its dual graph at the same time: it is the Tutte polynomial. The purpose of this seminar is to expose the mathematical richness of that polynomial. It reveals more of the internal structure of a graph, and even contains other specializations from other sciences such as the Jones polynomials from knot theory and the partition functions of the Potts model from statistical physics. But this seminar devotes more time to the hyperplane arrangements. In 2007, Ardila extended the notion of Tutte polynomial to real hyperplane arrangements. He particularly computed the Tutte polynomials of the classical Weyl arrangements. Those of the exceptional Weyl arrangements were computed by De Concini and Procesi one year later. One important specialization of the Tutte polynomial is the characteristic polynomial of hyperplane arrangements. The latter permits to deduce the number of regions, and the sum of their volume ratio, but that list is naturally not exhaustive. We describe our results which concern the Tutte polynomials associated to the imprimitive reflection groups, and to the ideals of root systems. Those results were established in 2017 and in 2018 respectively. Finally, we present some research projects. One part is a continuity of our results. The other part wishes to investigate derivatives of the Tutte polynomial which are the arithmetic Tutte polynomial, and the G-Tutte polynomial.
Date: Mercredi 10 Avril 2019 à 15 heures
Intervenant: Fabien Pazuki
Salle: Bibliothèque des Mathématiques
Résumé : Soit A une variété abélienne définie sur un corps de nombres. On montre que la hauteur de Faltings de A est essentiellement minorée par le logarithme de la norme des premiers de mauvaise réduction de A. La preuve proposée ici repose fortement sur le cas des variétés jacobiennes. L'exposé se voudra accessible et une grande partie des définitions seront rappelées et illustrées.
Mar: 9h00: Hugues Randriambololona (1) Analogies entre corps de nombres, corps de fonctions, et codes
Mar 10h30-11h30 Fabien Pazuki (1) Introduction aux courbes elliptiques.
Mar 14h-15h Christallin Razafindramahatsioro (1) Lifting problem on auto morphism groups of cyclic curves
Mer 9h00: Fabien Pazuki (2) Invariants modulaires et isogénies.
Mer 10h30-11h30 : Hughes Randriambololona (2) Construction de diviseurs non-spéciaux sur les courbes et rang tensoriel de la multiplication dans les corps finis.
Salle : IREM et Bibliothèeque des Mathématiques.
Renseignements : F. Patrick Rabarison - Bureau R 217
Departement de Math ́ematiques et Informatique
Faculté des Sciences – Université d’Antananarivo