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Добірка наукової літератури з теми "Sous-groupes modulaires"
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Статті в журналах з теми "Sous-groupes modulaires"
Mabilat, Flavien. "Combinatoire des sous-groupes de congruence du groupe modulaire." Annales Mathématiques Blaise Pascal 28, no. 1 (January 21, 2022): 7–43. http://dx.doi.org/10.5802/ambp.398.
Повний текст джерелаMabilat, Flavien. "Combinatoire des sous-groupes de congruence du groupe modulaire II." Annales Mathématiques Blaise Pascal 28, no. 2 (April 14, 2022): 199–229. http://dx.doi.org/10.5802/ambp.404.
Повний текст джерелаДисертації з теми "Sous-groupes modulaires"
Dostert, Mike. "Formes modulaires et courbes modulaires : quelques contributions à leur rôle en physique mathématique." Thesis, Metz, 2009. http://www.theses.fr/2009METZ050S.
Повний текст джерелаThe goal of this thesis is to analyze and to develop the mathematical objects that appeared in "New classical limits of quantum theories" of S. G. Rajeev, especially the (loc. sit) "neoclassical limits" in the context of the contexte of the theory of modular forms. To see what are the objects involved in the study of Rajeev, we constructed certain toy models where could develop similar calculations as those done in the article mentioned above. This was done by trying to compare these toy models with rigorous mathematical theories, for example Kähler quantization, algebric geometry and the trace formula for Hecke operators. After that we developed a rigorous mathematical frame where the objects introduced by Rajeev naturally live. This frame should be used in the futur to do the "neoclassical limit" calculations in this context. So the objects developed could be used by the mathematicians to understand the physical ideas and by the physicists to push further the calculations of perturbation
Dostert, Mike. "Formes modulaires et courbes modulaires : quelques contributions à leur rôle en physique mathématique." Electronic Thesis or Diss., Metz, 2009. http://www.theses.fr/2009METZ050S.
Повний текст джерелаThe goal of this thesis is to analyze and to develop the mathematical objects that appeared in "New classical limits of quantum theories" of S. G. Rajeev, especially the (loc. sit) "neoclassical limits" in the context of the contexte of the theory of modular forms. To see what are the objects involved in the study of Rajeev, we constructed certain toy models where could develop similar calculations as those done in the article mentioned above. This was done by trying to compare these toy models with rigorous mathematical theories, for example Kähler quantization, algebric geometry and the trace formula for Hecke operators. After that we developed a rigorous mathematical frame where the objects introduced by Rajeev naturally live. This frame should be used in the futur to do the "neoclassical limit" calculations in this context. So the objects developed could be used by the mathematicians to understand the physical ideas and by the physicists to push further the calculations of perturbation
Blossier, Thomas. "Ensembles minimaux localement modulaires : groupes d'automorphismes d'ensembles triviaux et sous-groupes infiniment définissables du groupe additif d'un corps séparablement clos." Paris 7, 2001. http://www.theses.fr/2001PA077172.
Повний текст джерелаSaadi, Fayssal. "Dynamique sur les espaces de modules." Electronic Thesis or Diss., Lyon, École normale supérieure, 2024. http://www.theses.fr/2024ENSL0039.
Повний текст джерелаIn this thesis, we are interested in the dynamics of the mapping class subgroups on the U(2) character variety. More precisely, we deal with ergodicity questions of a subgroup G of the mapping class group Mod(g,n) of a compact surface S(g,n) of genus g and n boundary components. These questions were naturally raised after Goldman's proof of the ergodicity of mapping class groups on the SU(2)-character variety. The first general result in this direction is due to Funar and Marché by showing that the first Johnson subgroups act ergodically on the character variety, for any closed surfaces S(g). On the other hand, Brown showed the existence of an elliptic fixed point (or a double elliptic fixed point) for any subgroup generated by a pseudo-Anosov element on the punctured torus S(1,1). This led to the proof of the non-ergodicity of such subgroups by Forni, Goldman, Lawton, and Mateus by applying KAM theory. In the first part of the thesis, we study the natural dynamics of the moduli space of spherical triangles on the 2-sphere relating these dynamics to the dynamics of the mapping class group on the SU(2)-character variety of the punctured torus.The second part is devoted to the study of the existence of elliptic fixed points for pseudo-Anosov homeomorphisms on the character varieties of punctured surfaces S(g,n), where g is 0 or 1. By showing that near any relative character variety of the once punctured torus, for a set of positive measure and dense of levels k, there exists a family of pseudo-Anosov elements that do not act ergodically on that level, in the case of the punctured torus S(1,1). A similar result holds for a set of parameters B in the case of the four-punctured sphere S(0,4). Then these results can be combined to construct a family of pseudo-Anosov elements on the twice-punctured torus S(1,2) that admit an elliptic fixed point.We discuss then the action of a group G generated by Dehn-twist along a pair of filling multi-curves or along a family of filling curves on S(g). We show in this part that there exist two filling multi-curves on the surface of genus two S(2) whose associated Dehn twists generate a group G acting non-ergodically on representation variety by finding explicit invariant rational functions. Similarly, We found invariant rational functions of a subgroup G generated by Dehn-twists along a family of filling loops on the character variety of the non-orientable surface of genus 4
Cumplido, Cabello María. "Sous-groupes paraboliques et généricité dans les groupes d'Artin-Tits de type sphérique." Thesis, Rennes 1, 2018. http://www.theses.fr/2018REN1S022/document.
Повний текст джерелаIn the first part of this thesis we study the genericity conjecture: In the Cayley graph of the mapping class group of a closed surface we look at a ball of large radius centered on the identity vertex, and at the proportion of pseudo-Anosov vertices among the vertices in this ball. The genericity conjecture states that this proportion should tend to one as the radius tends to infinity. We prove that it stays bounded away from zero and prove similar results for a large class of subgroups of the mapping class group. We also present analogous results for Artin--Tits groups of spherical type, knowing that in this case being pseudo-Anosov is analogous to being a loxodromically acting element. In the second part we provide results about parabolic subgroups of Artin-Tits groups of spherical type: The minimal standardizer of a curve on a punctured disk is the minimal positive braid that transforms it into a round curve. We give an algorithm to compute it in a geometrical way. Then, we generalize this problem algebraically to parabolic subgroups of Artin--Tits groups of spherical type. We also show that the intersection of two parabolic subgroups is a parabolic subgroup and that the set of parabolic subgroups forms a lattice with respect to inclusion. Finally, we define the simplicial complex of irreducible parabolic subgroups, and we propose it as the analogue of the curve complex for mapping class groups