In this thesis we study several properties of finitely presented groups, through the unifying paradigm of encoding sought-after group properties into presentations and detecting group properties from presentations, in the context of Geometric Group Theory. A group law is said to be detectable in power subgroups if, for all coprime m and n, a group G satisfies the law if and only if the power subgroups G(^m) and G(ⁿ) both satisfy the law. We prove that for all positive integers c, nilpotency of class at most c is detectable in power subgroups, as is the k-Engel law for k at most 4. In contrast, detectability in power subgroups fails for solvability of given derived length: we construct a finite group W such that W(²) and W(³) are metabelian but W has derived length 3. We analyse the complexity of the detectability of commutativity in power subgroups, in terms of finite presentations that encode a proof of the result. We construct a census of two-generator one-relator groups of relator length at most 9, with complete determination of isomorphism type, and verify a conjecture regarding conditions under which such groups are automatic. Furthermore, we introduce a family of one-relator groups and classify which of them act properly cocompactly on complete CAT(0) spaces; the non-CAT(0) examples are counterexamples to a variation on the aforementioned conjecture. For a subclass, we establish automaticity, which is needed for the census. The deficiency of a group is the maximum over all presentations for that group of the number of generators minus the number of relators. Every finite group has non-positive deficiency. For every prime p we construct finite p-groups of arbitrary negative deficiency, and thereby complete Kotschick's proposed classification of the integers which are deficiencies of Kähler groups. We explore variations and embellishments of our basic construction, which require subtle Schur multiplier computations, and we investigate the conditions on inputs to the construction that are necessary for success. A well-known question asks whether any two non-isometric finite volume hyperbolic 3-manifolds are distinguished from each other by the finite quotients of their fundamental groups. At present, this has been proved only when one of the manifolds is a once-punctured torus bundle over the circle. We give substantial computational evidence in support of a positive answer, by showing that no two manifolds in the SnapPea census of 72 942 finite volume hyperbolic 3-manifolds have the same finite quotients. We determine examples of sizeable graphs, as required to construct finitely presented non-hyperbolic subgroups of hyperbolic groups, which have the fewest vertices possible modulo mild topological assumptions.

Submitted by ANA KARLA PEREIRA RODRIGUES (anakarla_@hotmail.com) on 2017-08-16T14:45:10Z No. of bitstreams: 1 arquivototal.pdf: 923276 bytes, checksum: 684d210a074aefcedef691723f8d04e0 (MD5) / Made available in DSpace on 2017-08-16T14:45:10Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 923276 bytes, checksum: 684d210a074aefcedef691723f8d04e0 (MD5) Previous issue date: 2016-03-18 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / It is well-known that planes and quadric surfaces in the projective space contain in - nitely many lines. For smooth cubic surface Cayley and Salmon, 1847, (and Clebsch later) proved that it has exactly 27 lines. For degree 4, in 1943 Segre proved that the maximum number of lines contained in a smooth quartic surface is 64. For surfaces of degree greater than 4 this number is unknown. In this work, we are going to explore what is the maximum number of lines that a smooth complex surface of degree d of the family Fd ; may contain. Thus, we obtain a lower bound to the maximum number of lines that non singular surfaces of degree d in P3 may contain. We emphasize that the determination of this numbers is based on the Klein's classi cation theorem of nitte subgroups of Aut(P1) and the study of 􀀀C; the subgroup of Aut(P1) whose elements leaves invariant the nite subset C of P1: / Sabe-se que planos e superf cies qu adricas no espa co projetivo cont em in nitas retas. No caso de uma superf cie c ubica n~ao singular Cayley e Salmon, em 1847, (e Clebsch, mais tarde) provaram que ela cont em exatamente 27 retas. No caso de grau 4, em 1943 Segre provou que o n umero m aximo de retas contidas numa superf cie qu artica n~ao singular e 64. Para superf cies de grau maior que 4 esse n umero e desconhecido. Neste trabalho vamos explorar qual e a quantidade m axima de retas que uma superf cie complexa n~ao singular de grau d na fam lia Fd ; pode conter. Assim obtemos uma cota inferior para o n umero m aximo de retas que as superf cies n~ao singulares de grau d em P3 podem conter. Salientamos que a determina c~ao destes n umeros tem como base o Teorema de Classi ca cao de Klein dos sugbrupos nitos de Aut(P1) e o estudo dos subgrupos 􀀀C de Aut(P1) que deixam invariante um subconjunto nito C de P1:

The clinical introduction of proton therapy requires an extensive analysis of its benefits compared to conventional radiotherapy and a detailed analysis of possible uncertainties which might have serious consequences for patient treatment. In the first part of the presented thesis, the expected toxicities were evaluated for a treatment of head and neck cancer patients using a biologically adapted dose escalation schedule with photon and proton therapy. The feasibility of the dose escalation schedule could be demonstrated for both photon and proton therapy, since only a small increase in toxicity risk occurred for most toxicities. However, the expected toxicity risks were in most cases smaller with proton therapy. Furthermore, a higher benefit was found for patients with primary tumour locations in the upper head and neck area, who thus might be preferably referred to proton therapy. In the second part of this thesis, an extensive analysis of the impact of tumour motion in lung cancer treatment with active-scanning proton therapy was conducted. It could be shown, that dose degradations were small for tumour motion amplitudes below 5 mm. Parameters like the target volume concept, the optimisation approach, changes in the motion pattern and application sequence times had additional impact on the dose degradation. However, their magnitude was patient specific. Since not all parameters can be assessed before treatment, e.g. the motion pattern during treatment, prospective estimations should be supplemented by retrospective analyses. / Die Einführung der Protonentherapie in die klinische Praxis erfordert umfassende Analysen ihrer Vor- und Nachteile im Vergleich zur konventionellen Photonentherapie sowie detaillierte Untersuchungen der Auswirkungen von Unsicherheiten in der Therapieapplikation. Im ersten Teil der vorliegenden Arbeit wurden die zu erwartenden Nebenwirkungen bei der Behandlung von Patienten mit Kopf-Hals-Tumoren mit einem biologisch-adaptierten Fraktionierungsschema inklusive Dosiseskalation mit Photonen- und Protonentherapie evaluiert. Dabei konnte gezeigt werden, dass die Dosiseskalation sowohl mit Photonen- als auch Protonentherapie angewandt werden kann, da die Wahrscheinlichkeit für das Auftreten von Nebenwirkungen in den meisten Fällen kaum erhöht wurde. Weiterhin wurden die Nebenwirkungswahrscheinlichkeiten mit der Protonentherapie im Vergleich zur Photonentherapie reduziert. Dies war vor allem für Patienten mit Tumoren im oberen Kopf-Hals-Bereich der Fall. Diese könnten daher bevorzugt zur Protonentherapie überwiesen werden. Darüber hinaus wurde im zweiten Teil der Arbeit eine umfassende Analyse des Einflusses der Tumorbewegung auf die Dosisverteilung bei Behandlung von Lungentumoren mit aktiver Protonenstrahlformierung durchgeführt. Dabei zeigte sich, dass Dosisdegradierungen bei Bewegungsamplituden unter 5mm gering sind. Parameter wie das Zielvolumenkonzept, Veränderungen des Bewegungsmusters oder der Applikationszeiten nehmen zusätzlich Einfluss auf die Dosisdegradierung, allerdings in unterschiedlichem Maß für individuelle Patienten. Da nicht alle Parameter vor Behandlung bekannt sein können, sollten prospektive Dosisabschätzungen durch retrospektive Analysen ergänzt werden.

Dans la première partie de cette thèse on étudiera la conjecture de généricité: dans le graphe de Cayley du groupe modulaire d'une surface fermée on regarde une boule centrée à l'identité et on s'intéresse à la proportion de sommets pseudo-Anosov dans cette boule. La conjecture de généricité affirme que cette proportion doit tendre vers 1 quand le rayon de la boule tend vers l'infini. On montre qu'elle est bornée inférieurement par un nombre strictement positif et on montre des résultats similaires pour une grande classe de sous-groupes du groupe modulaire. On présente aussi des résultats analogues pour des groupes d'Artin-Tits de type sphérique, en sachant que dans ce cas, être pseudo-Anosov est analogue à agir loxodromiquement sur un complexe delta-hyperbolique convenable. Dans la deuxième partie on donne des résultats sur les sous-groupes paraboliques des groupes d'Artin-Tits de type sphérique: le standardisateur minimal d'une courbe dans le disque troué est la tresse minimale positive qui la fait devenir ronde. On construit un algorithme pour le calculer d'une façon géométrique. Ensuite, on généralise le problème pour les groupes d'Artin-Tits de type sphérique. On montre aussi que l'intersection de deux sous-groupes paraboliques est un sous-groupe parabolique et que l'ensemble de sous-groupes paraboliques est un treillis par rapport à l'inclusion. Finalement, on définit le complexe simplicial des sous-groupes paraboliques irréductibles, et on le propose comme l'analogue du complexe de courbes. / In 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.

The clinical introduction of proton therapy requires an extensive analysis of its benefits compared to conventional radiotherapy and a detailed analysis of possible uncertainties which might have serious consequences for patient treatment. In the first part of the presented thesis, the expected toxicities were evaluated for a treatment of head and neck cancer patients using a biologically adapted dose escalation schedule with photon and proton therapy. The feasibility of the dose escalation schedule could be demonstrated for both photon and proton therapy, since only a small increase in toxicity risk occurred for most toxicities. However, the expected toxicity risks were in most cases smaller with proton therapy. Furthermore, a higher benefit was found for patients with primary tumour locations in the upper head and neck area, who thus might be preferably referred to proton therapy. In the second part of this thesis, an extensive analysis of the impact of tumour motion in lung cancer treatment with active-scanning proton therapy was conducted. It could be shown, that dose degradations were small for tumour motion amplitudes below 5 mm. Parameters like the target volume concept, the optimisation approach, changes in the motion pattern and application sequence times had additional impact on the dose degradation. However, their magnitude was patient specific. Since not all parameters can be assessed before treatment, e.g. the motion pattern during treatment, prospective estimations should be supplemented by retrospective analyses. / Die Einführung der Protonentherapie in die klinische Praxis erfordert umfassende Analysen ihrer Vor- und Nachteile im Vergleich zur konventionellen Photonentherapie sowie detaillierte Untersuchungen der Auswirkungen von Unsicherheiten in der Therapieapplikation. Im ersten Teil der vorliegenden Arbeit wurden die zu erwartenden Nebenwirkungen bei der Behandlung von Patienten mit Kopf-Hals-Tumoren mit einem biologisch-adaptierten Fraktionierungsschema inklusive Dosiseskalation mit Photonen- und Protonentherapie evaluiert. Dabei konnte gezeigt werden, dass die Dosiseskalation sowohl mit Photonen- als auch Protonentherapie angewandt werden kann, da die Wahrscheinlichkeit für das Auftreten von Nebenwirkungen in den meisten Fällen kaum erhöht wurde. Weiterhin wurden die Nebenwirkungswahrscheinlichkeiten mit der Protonentherapie im Vergleich zur Photonentherapie reduziert. Dies war vor allem für Patienten mit Tumoren im oberen Kopf-Hals-Bereich der Fall. Diese könnten daher bevorzugt zur Protonentherapie überwiesen werden. Darüber hinaus wurde im zweiten Teil der Arbeit eine umfassende Analyse des Einflusses der Tumorbewegung auf die Dosisverteilung bei Behandlung von Lungentumoren mit aktiver Protonenstrahlformierung durchgeführt. Dabei zeigte sich, dass Dosisdegradierungen bei Bewegungsamplituden unter 5mm gering sind. Parameter wie das Zielvolumenkonzept, Veränderungen des Bewegungsmusters oder der Applikationszeiten nehmen zusätzlich Einfluss auf die Dosisdegradierung, allerdings in unterschiedlichem Maß für individuelle Patienten. Da nicht alle Parameter vor Behandlung bekannt sein können, sollten prospektive Dosisabschätzungen durch retrospektive Analysen ergänzt werden.

We study two topics on surface diffeomorphisms, their mapping classes and dynamics. For the mapping classes of a punctured disc, we study the $\ZxZ$ subgroups of the fundamental groups of the corresponding mapping tori. An application is the proof of the fact that a satellite knot with braid pattern is prime. For the mapping classes of the disc minus a Cantor set, we study a special type of reducible mapping class. This has direct application on the embeddings of solenoids in $\mathbb{S}^3$. We also give some examples of other types of mapping classes of the disc minus a Cantor set. For the dynamics of surface diffeomorphisms, we prove three formulas for computing the topological pressure of a $C^1$-generic conservative diffeomorphism with no dominated splitting and show the continuity of topological pressure with respect to these diffeomorphisms. We prove for these generic diffeomorphisms that there is no equilibrium states with positive measure theoretic entropy. In particular, for hyperbolic potentials, there are no equilibrium states. For $C^1$ generic conservative diffeomorphisms on compact surfaces with no dominated splitting and $\phi_m(x):=-\frac{1}{m}\log \Vert D_x f^m\Vert, m \in \mathbb{N}$, we show that there exist equilibrium states with zero entropy and there exists a transition point $t_0$ for the one parameter family $\lbrace t \phi_m\rbrace_{t\geq 0}$, such that there is no equilibrium states for $ t \in [0, t_0)$ and there is an equilibrium state for $t \in [t_0,+\infty)$.

T-cell prolymphocytic leukemia (T-PLL) is a rare blood cancer with poor prognosis. Overexpression of the proto-oncogene TCL1A and missense mutations of the tumor suppressor ATM are putative main drivers of T-PLL development, but so far only little is known about the existence of T-PLL gene expression subtypes. We performed an in-depth computational reanalysis of 68 gene expression profiles of one of the largest currently existing T-PLL patient cohorts. Hierarchical clustering combined with bootstrapping revealed three robust T-PLL gene expression subgroups. Additional comparative analyses revealed similarities and differences of these subgroups at the level of individual genes, signaling and metabolic pathways, and associated gene regulatory networks. Differences were mainly reflected at the transcriptomic level, whereas gene copy number profiles of the three subgroups were much more similar to each other, except for few characteristic differences like duplications of parts of the chromosomes 7, 8, 14, and 22. At the network level, most of the 41 predicted potential major regulators showed subgroup-specific expression levels that differed at least in comparison to one other subgroup. Functional annotations suggest that these regulators contribute to differences between the subgroups by altering processes like immune responses, angiogenesis, cellular respiration, cell proliferation, apoptosis, or migration. Most of these regulators are known from other cancers and several of them have been reported in relation to leukemia (e.g. AHSP, CXCL8, CXCR2, ELANE, FFAR2, G0S2, GIMAP2, IL1RN, LCN2, MBTD1, PPP1R15A). The existence of the three revealed T-PLL subgroups was further validated by a classification of T-PLL patients from two other smaller cohorts. Overall, our study contributes to an improved stratification of T-PLL and the observed subgroup-specific molecular characteristics could help to develop urgently needed targeted treatment strategies.

Thèse numérisée par la Direction des bibliothèques de l'Université de Montréal.

Une approche inductive est développée pour la théorie des représentations de la chaîne des algèbres de Hecke cyclotomiques de type G(m,1,n). Cette approche repose sur l'étude du spectre d'une famille commutative maximale, formée par les analogues des éléments de Jucys--Murphy.Les représentations irréductibles, paramétrées par les multi-partitions, sont construites avec l'aide d'une nouvelle algèbre associative, dont l'espace vectoriel sous-jacent est le produit tensoriel de l'algèbre de Hecke cyclotomique avec l'algèbre associative libre engendrée par les multi-tableaux standards.L'analogue de cette approche est présentée pour la limite classique, c'est-à-dire la chaîne des groupes de réflexions complexes de type G(m,1,n).Dans une seconde partie, une base des algèbres de Hecke cyclotomiques est donnée et la platitude de la déformation est montrée sans utiliser la théorie des représentations. Ces résultats sont généralisés aux algèbres de Hecke affines de type A.Ensuite, une procédure de fusion est présentée pour les groupes de réflexions complexes et les algèbres de Hecke cyclotomiques de type G(m,1,n). Dans les deux cas, un ensemble complet d'idempotents primitifs orthogonaux est obtenu par évaluation consécutive d'une fonction rationnelle.Dans une troisième partie, une nouvelle présentation est obtenue pour les sous-groupes alternés de tous les groupes de Coxeter. Les générateurs sont reliés aux arêtes orientées du graphe de Coxeter. Cette présentation est ensuite étendue, pour tous les types, aux extensions spinorielles des groupes alternés, aux algèbres de Hecke alternées et aux sous-groupes alternés des groupes de tresses. / An inductive approach to the representation theory of the chain of the cyclotomic Hecke algebras of type G(m,1,n) is developed. This approach relies on the study of the spectrum of a maximal commutative family formed by the analogues of the Jucys--Murphy elements.The irreducible representations, labelled by the multi-partitions, are constructed with the help of a new associative algebra, whose underlying vector space is the tensor product of the cyclotomic Hecke algebra with the free associative algebra generated by the standard multi-tableaux.The analogue of this approach is presented for the classical limit, that is for the chain of complex reflection groups of type G(m,1,n).In a second part, a basis of the cyclotomic Hecke algebras is given and the flatness of the deformation is proved without using the representation theory. These results are extended to the affine Hecke algebras of type A.Then a fusion procedure is presented for the complex reflection groups and the cyclotomic Hecke algebras of type G(m,1,n). In both cases, a complete set of primitive orthogonal idempotents is obtained by successive evaluations of a rational fonction.In a third part, a new presentation is obtained for the alternating subgroups of all Coxeter groups. The generators are related to oriented edges of the Coxeter graph. This presentation is then extended, for all types, to the spinor extensions of the alternating groups, the alternating Hecke algebras and the alternating subgroups of braid groups.

Pour tout entier naturel impair d, on construit un domaine fondamental pour l'action sur l'espace affine de dimension 2d+1 de certains groupes de transformations affines libres non abéliens, discrets, agissant proprement et de partie linéaire Zariski-dense dans SO(d+1, d). Pour tout groupe de Lie semisimple réel non compact G, on construit ensuite un groupe de transformations affines de son algèbre de Lie g qui est libre non abélien, discret, agit proprement sur g et a sa partie linéaire Zariski-dense dans Ad G. Enfin, on donne quelques résultats sur le comportement local des fonctions harmoniques sur le triangle de Sierpinski, plus précisément de leur restriction à un bord du triangle. / For every odd positive integer d, we construct a fundamental domain for the action on the 2d+1-dimensional space of certain groups of affine transformations which are free, nonabelian, act properly discontinuously and have linear part Zariski-dense in SO(d+1,d). Next for every semisimple noncompact real Lie group G, we construct a group of affine transformations of its Lie algebra g which is free, nonabelian, acts properly discontinuously and has linear part Zariski-dense in Ad G. Finally, we give some results about the local behavior of harmonic functions on the Sierpinski triangle restricted to a side of the triangle.