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Winfried Kohnen (Universität Heidelberg)23/06/2014 10:00Analytic-Additive Number TheoryWe will give a survey on recent results about sign changes of Fourier coefficients of cusp forms in one and several variables.Aller à la page de la contribution
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Lilian Matthiesen (Institut de Mathématiques de Jussieu)23/06/2014 11:30Analytic-Additive Number TheoryThe aim of this talk is to explain a strategy that allows us to bound the Fourier coefficients of a large class of not necessarily bounded multiplicative functions. The interest in this result lies in the fact that the strategy can be adapted to show that these multiplicative functions give rise to functions that are orthogonal to linear nilsequences when applying a `W-trick'. This, in turn,...Aller à la page de la contribution
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Catherine Goldstein (Institut de mathématiques de Jussieu)23/06/2014 14:30Analytic-Additive Number TheoryContrarily to other parts of number theory, the history of analytic number theory often appears as a collection of particular, even isolated, episodes, focussing on Euler or Riemann or Hadamard and de La Vallée-Poussin. The talk will discuss some of these gems, as well as less well-known ones, and comment on the discontinuous character of their history.Aller à la page de la contribution
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Julio Andrade (IHES)23/06/2014 15:45Analytic-Additive Number TheoryIn this talk I will explore some traditional problems of analytic number theory in the context of function fields over a finite field. Several such problems which are currently viewed as intractable can, in the function field scenario, be attacked with vastly different tools than those of traditional analytic number theory. The resulting theorems in the function field setting can be used to...Aller à la page de la contribution
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Alain Plagne (École polytechnique)23/06/2014 17:15Analytic-Additive Number TheoryNous étudions des phénomènes de seuil en théorie additive des nombres. L'objet central est les pseudo puissances s-ièmes introduites par Erdos et Renyi en 1960. In 1975, Goguel a montré que, presque surement, une telle suite n'était pas une base asymptotique d'ordre s. On verra qu'elle est presque surement base d'ordre s+\epsilon. On étudie aussi la taille du plus petit complément additif de...Aller à la page de la contribution
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Gebhard Boeckle (Heidelberg University)24/06/2014 09:00Galois representations and modular formsRecently Dorobisz, Eardley-Manoharmayum and Manoharmayum have proved abstract results (a) on the shape of possible deformation rings and (b) on the image of universal deformations of profinite groups, for representations into GL_n. The result regarding (a) were motivated by questions of Bleher, Chinburg and de Smit. We place these results in an axiomatic framework that in principle applies to...Aller à la page de la contribution
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François Brunault (École normale supérieure de Lyon)24/06/2014 10:30Galois representations and modular formsAn abelian variety defined over a number field is called strongly modular when its L-function is the product of L-functions of modular forms of weight 2. In this talk, we will show a weak version of Beilinson's conjectures for non-critical L-values of strongly modular abelian varieties. We will explain the interest of formulating an equivariant version of these conjectures (after Burns and...Aller à la page de la contribution
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Nicolas Billerey (Université Clermont-Ferrand 2)24/06/2014 11:45Galois representations and modular formsIn this talk, I'll give a modularity result for reducible mod l Galois representations. By analogy with the irreducible case, I'll state some questions regarding characterization and optimization of the different types of modular forms attached to such a given representation. Finally, I'll give an application of these results to the determination of an explicit lower bound for the highest...Aller à la page de la contribution
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Luis Dieulefait (Universitat de Barcelona)24/06/2014 15:30Galois representations and modular formsThis is joint work with Ariel Pacetti. We present generalizations to totally real number fields of the construction done by the speaker some years ago over Q that allows to connect to each other any given pair of newforms through chains of modular compatible systems of Galois representations. We also discuss applications of this, and we consider the case of abstract Galois representations and...Aller à la page de la contribution
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Gabor Wiese (Université du Luxembourg)24/06/2014 17:00Galois representations and modular formsIn the talk I will report on recent results on the inverse Galois problem based on compatible systems of Galois representations coming from modular and automorphic forms. The focus will be on ideas and strategies as well as the obstacles that are preventing us from proving much stronger theorems. In this context, the role of coefficient fields will be particularly highlighted. Most parts are...Aller à la page de la contribution
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Walter Ferrer-Santos (Universidad de la Republica, Montevideo)25/06/2014 09:00Noncommutative algebraAn involutory Hopf algebra is a Hopf algebra whose antipode squared equals the identity, $S^2=\operatorname{id}$. The identity map is an automorphism of Hopf algebras, hence it is tempting to substitute $\operatorname{id} \mapsto \sigma$ where $\sigma$ is an arbitray Hopf morphism and consider Hopf algebras whose antipode (that is an antimorphism of Hopf algebras) squared is the square of...Aller à la page de la contribution
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Alberto Facchini (University of Padova)25/06/2014 10:30Noncommutative algebraWe will describe direct-sum decompositions and direct-product decompositions for some classes of modules. We will be mainly interested in direct sums and direct products of modules whose endomorphism rings have at most two maximal ideals.Aller à la page de la contribution
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Patrick Solé (Telecom ParisTech)25/06/2014 11:45Noncommutative algebraIn this article we introduce skew generalized quasi-cyclic codes over finite field $F$ with Galois automorphism $\theta$. This is a generalization of quasi-cyclic codes and skew polynomial codes. These codes have an added advantage over quasi-cyclic codes, since the length of the code $C$ need not be a multiple of the index of $C$. After a brief description of the skew polynomial ring...Aller à la page de la contribution
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Olivier Wittenberg (École normale supérieure)26/06/2014 09:00Arithmetic geometry and Galois theorySi X est une variété projective et lisse définie sur un corps de nombres, la ``méthode des fibrations'' pour étudier l'ensemble des points rationnels de X ou le groupe de Chow des zéro-cycles de X vise à ramener les questions que l'on pose pour X (par exemple: existence d'un point ou d'un zéro-cycle de degré 1) aux mêmes questions pour les fibres d'un morphisme dominant f:X->P^1. Le but de...Aller à la page de la contribution
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David Harbater (University of Pennsylvania)26/06/2014 10:30Arithmetic geometry and Galois theoryThe Oort conjecture states that every cyclic branched cover of curves in characteristic p can be lifted to such a cover in characteristic zero. This raises the more general question of which finite groups G have the property that every G-Galois branched cover of curves in characteristic p can be lifted to characteristic zero. While this can be viewed as analogous to the inverse Galois...Aller à la page de la contribution
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David Harari (Université Paris-Sud)26/06/2014 11:45Let T be an algebraic torus defined over a number field K. In the case of a number field, obstructions to local-global principles for T are well understood thanks to work by Voskresenskii and Sansuc. We consider the case K=k(t) for different fields k (quasi-finite, p-adic) and extend the classical results in this context.Aller à la page de la contribution
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Lorenzo Ramero (Université Lille 1)26/06/2014 15:30Arithmetic geometry and Galois theoryScholze's theory of perfectoid rings and perfectoid spaces is rather recent, but it has already had some spectacular applications to étale cohomology, p-adic Hosge theory and p-adic representations. I will present a generalization of this theory that I am developing in collaboration with Ofer Gabber. I will also explain the questions that have led us to this generalization.Aller à la page de la contribution
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Aaron Silberstein (University of Pennsylvania)26/06/2014 17:00Arithmetic geometry and Galois theoryGiven a field $K$, finitely generated and of transcendence degree $2$ over the algebraic closure of a prime field, we may now reconstruct $K$ from the maximal $2$-step nilpotent pro-$\ell$ quotient of its absolute Galois group. This allows us to construct a complete (albeit countably infinite) set of geometric obstructions for an element of the Grothendieck-Teichmüller group to come from an...Aller à la page de la contribution
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Alexander Vishik (University of Nottingham)27/06/2014 09:00Quadratic formsThis is a joint work with Alexander Smirnov. I will describe a new homotopic approach to the classification of torsors of algebraic Groups. It extends the approach of Morel-Voevodsky, where torsors are interpreted as Hom’s to the classifying space of the group in the A^1-homotopy category of Morel-Voevodsky. In the case of the orthogonal group O(n), we introduce new invariants: “Subtle...Aller à la page de la contribution
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Bruno Kahn (Institut de Mathématiques de Jussieu)27/06/2014 10:30Quadratic formsOn définit une notion de réciprocité sur les préfaisceaux avec transferts (PST) de Voevodsky. Pour cela, on enrichit les groupes de 0-cycles avec module de Kerz-Saito en leur conférant une structure de PST. Les PST invariants par homotopie sont à réciprocité, ainsi que ceux représentables par un groupe algébrique commutatif : ce dernier point généralise un théorème classique de Rosenlicht qui...Aller à la page de la contribution
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Jean-Pierre Tignol (Université catholique de Louvain)27/06/2014 11:45Quadratic formsLa dimension, le discriminant, et l'invariant de Clifford sont des invariants classiques des formes quadratiques, qui s'étendent au contexte plus général des algèbres centrales simples à involution orthogonale. Sous certaines conditions, on peut aussi définir un invariant d'Arason; mais contrairement à ce qui se passe pour les formes quadratiques, celui-ci n'est pas toujours représenté par une...Aller à la page de la contribution
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