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# Documents : Multi angle  Conférences Vidéo | enregistrements trouvés : 200

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## Besov spaces in multifractal environment, and the Frisch-Parisi conjecture Seuret, Stéphane | CIRM H

Multi angle

Research talks

Multifractal properties of data coming from many scientific fields (especially in turbulence) are now rigorously established. Unfortunately, the parameters measured on these data do not correspond to those mathematically obtained for the typical (or almost sure) functions in the standard functional spaces: Hölder, Sobolev, Besov…
In this talk, we introduce very natural Besov spaces in which typical functions possess very rich scaling properties, mimicking those observed on data for instance. We obtain various characterizations of these function spaces, in terms of oscillations or wavelet coefficients.
Combining this with the construction of almost-doubling measures with prescribed scaling properties, we are able to bring a solution to the so-called Frisch-Parisi conjecture. This is a joint work with Julien Barral (Université Paris-Nord).
Multifractal properties of data coming from many scientific fields (especially in turbulence) are now rigorously established. Unfortunately, the parameters measured on these data do not correspond to those mathematically obtained for the typical (or almost sure) functions in the standard functional spaces: Hölder, Sobolev, Besov…
In this talk, we introduce very natural Besov spaces in which typical functions possess very rich scaling properties, ...

37F35

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## Marked length spectrum rigidity and the geodesic stretch Knieper, Gerhard | CIRM H

Multi angle

Research talks

Joint work with Guillarmou and Lefeuvre.

37D40

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## Intermediate dimensions, capacities and projections Falconer, Kenneth | CIRM H

Multi angle

Research talks

The talk will review recent work on intermediate dimensions which interpolate between Hausdorff and box dimensions. We relate these dimensions to capacities which leading to ‘Marstrand-type’ theorems on the intermediate dimensions of projections of a set in $\mathbb{R}^{n}$ onto almost all m-dimensional subspaces. This is collaborative work with various combinations of Stuart Burrell, Jonathan Fraser, Tom Kempton and Pablo Shmerkin.

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## Closed geodesics and the measure of maximal entropy on surfaces without conjugate points Climenhaga, Vaughn | CIRM H

Multi angle

Research talks

For negatively curved Riemannian manifolds, Margulis gave an asymptotic formula for the number of closed geodesics with length below a given threshold. I will describe joint work with Gerhard Knieper and Khadim War in which we obtain the corresponding result for surfaces without conjugate points by first proving uniqueness of the measure of maximal entropy and then following the approach of recent work by Russell Ricks, who established the asymptotic estimates in the setting of CAT(0) geodesic flows. For negatively curved Riemannian manifolds, Margulis gave an asymptotic formula for the number of closed geodesics with length below a given threshold. I will describe joint work with Gerhard Knieper and Khadim War in which we obtain the corresponding result for surfaces without conjugate points by first proving uniqueness of the measure of maximal entropy and then following the approach of recent work by Russell Ricks, who established the ...

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## Prime numbers with preassigned digits Swaenepoel, Cathy | CIRM H

Multi angle

Research talks

Bourgain (2015) estimated the number of prime numbers with a proportion $c$ > 0 of preassigned digits in base 2 ($c$ is an absolute constant not specified). We present a generalization of this result in any base $g$ ≥ 2 and we provide explicit admissible values for the proportion $c$ depending on $g$. Our proof, which adapts, develops and refines Bourgain’s strategy, is based on the circle method and combines techniques from harmonic analysis together with results on zeros of Dirichlet $L$-functions, notably a very sharp zero-free region due to Iwaniec. Bourgain (2015) estimated the number of prime numbers with a proportion $c$ > 0 of preassigned digits in base 2 ($c$ is an absolute constant not specified). We present a generalization of this result in any base $g$ ≥ 2 and we provide explicit admissible values for the proportion $c$ depending on $g$. Our proof, which adapts, develops and refines Bourgain’s strategy, is based on the circle method and combines techniques from harmonic analysis ...

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## Monogenic cubic fields and local obstructions Shnidman, Ari | CIRM H

Multi angle

Research talks

A number field is monogenic if its ring of integers is generated by a single element. It is conjectured that for any degree d > 2, the proportion of degree d number fields which are monogenic is 0. There are local obstructions that force this proportion to be < 100%, but beyond this very little is known. I’ll discuss work with Alpoge and Bhargava showing that a positive proportion of cubic fields (d = 3) have no local obstructions and yet are still not monogenic. This uses new results on ranks of Selmer groups of elliptic curves in twist families. A number field is monogenic if its ring of integers is generated by a single element. It is conjectured that for any degree d > 2, the proportion of degree d number fields which are monogenic is 0. There are local obstructions that force this proportion to be < 100%, but beyond this very little is known. I’ll discuss work with Alpoge and Bhargava showing that a positive proportion of cubic fields (d = 3) have no local obstructions and yet are ...

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Multi angle

Research talks

In this talk I will discuss questions concerning the asymptotic behavior of the Epstein zeta function $E_{n}\left ( L, s \right )$ in the limit of large dimension $n$. In particular I will be interested in the behavior of $E_{n}\left ( L, s \right )$ for a random lattice $L$ of large dimension $n$ and $s$ a complex number in the critical strip. Along the way we will encounter certain random functions that are closely related to $E_{n}\left ( L, s \right )$ and interesting in their own right. In this talk I will discuss questions concerning the asymptotic behavior of the Epstein zeta function $E_{n}\left ( L, s \right )$ in the limit of large dimension $n$. In particular I will be interested in the behavior of $E_{n}\left ( L, s \right )$ for a random lattice $L$ of large dimension $n$ and $s$ a complex number in the critical strip. Along the way we will encounter certain random functions that are closely related to $E_{n}\left ( L, ... Déposez votre fichier ici pour le déplacer vers cet enregistrement. ## Possibles et impossibles en mathématiques Banderier, Cyril | CIRM H Multi angle Outreach;Mathematics Education and Popularization of Mathematics;Mathematics in Science and Technology Déposez votre fichier ici pour le déplacer vers cet enregistrement. ## The essential skeletons of pairs and the geometric P=W conjecture Mauri, Mirko | CIRM H Multi angle Research talks The geometric P=W conjecture is a conjectural description of the asymptotic behavior of a celebrated correspondence in non-abelian Hodge theory. In particular, it is expected that the dual boundary complex of the compactification of character varieties is a sphere. In a joint work with Enrica Mazzon and Matthew Stevenson, we manage to compute the first non-trivial examples of dual complexes in the compact case. This requires to develop a new theory of essential skeletons over a trivially-valued field. As a byproduct, inspired by these constructions, we show that certain character varieties appear in degenerations of compact hyper-Kähler manifolds. In this talk we will explain how these new non-archimedean techniques can shed new light into classical algebraic geometry problems. The geometric P=W conjecture is a conjectural description of the asymptotic behavior of a celebrated correspondence in non-abelian Hodge theory. In particular, it is expected that the dual boundary complex of the compactification of character varieties is a sphere. In a joint work with Enrica Mazzon and Matthew Stevenson, we manage to compute the first non-trivial examples of dual complexes in the compact case. This requires to develop a new ... 14G22 Déposez votre fichier ici pour le déplacer vers cet enregistrement. ## Representation varieties of fundamental groups of complex algebraic varieties and mixed Hodge structures Lefèvre, Louis-Clément | CIRM H Multi angle Research talks We study locally the representation varieties of fundamental groups of smooth complex algebraic varieties. These are schemes whose complex points parametrize such representations into linear algebraic groups. At a given representation, the structure of the formal local ring to the representation variety tells about the obstructions to deform formally this representation, which is ultimately related to topological obstructions to the possible fundamental groups of complex algebraic varieties. This was first described by Goldman and Millson in the case of compact Kähler manifold, using formal deformation theory and differential graded Lie algebras. We review this using methods of Hodge theory and of derived deformation theory and we are able to describe locally the representation variety for non-compact smooth varieties and representations underlying a variation of Hodge structure. We study locally the representation varieties of fundamental groups of smooth complex algebraic varieties. These are schemes whose complex points parametrize such representations into linear algebraic groups. At a given representation, the structure of the formal local ring to the representation variety tells about the obstructions to deform formally this representation, which is ultimately related to topological obstructions to the possible ... Déposez votre fichier ici pour le déplacer vers cet enregistrement. ## Rational curves on K3 surfaces Gounelas, Frank | CIRM H Multi angle Research talks Bogomolov and Mumford proved that every complex projective K3 surface contains a rational curve. Since then, a lot of progress has been made by Bogomolov, Chen, Hassett, Li, Liedtke, Tschinkel and others, towards the stronger statement that any such surface in fact contains infinitely many rational curves. In this talk I will present joint work with Xi Chen and Christian Liedtke completing the remaining cases of this conjecture, reproving some of the main previously known cases more conceptually and extending the result to arbitrary genus in a suitable sense. Bogomolov and Mumford proved that every complex projective K3 surface contains a rational curve. Since then, a lot of progress has been made by Bogomolov, Chen, Hassett, Li, Liedtke, Tschinkel and others, towards the stronger statement that any such surface in fact contains infinitely many rational curves. In this talk I will present joint work with Xi Chen and Christian Liedtke completing the remaining cases of this conjecture, reproving some ... 14J28 Déposez votre fichier ici pour le déplacer vers cet enregistrement. ## Momentum polytopes of Kähler compact multiplicity-free manifolds Cupit-Foutou, Stéphanie | CIRM H Multi angle Research talks I will present some results about the momentum polytopes of the multiplicity-free Hamiltonian compact manifolds acted on by a compact group which are Kählerizable. I shall give a characterization of these polytopes, explain how much they determine these manifolds and sketch some applications of this characterization - most of these results have been obtained jointly with G. Pezzini and B. Van Steirteghem. Déposez votre fichier ici pour le déplacer vers cet enregistrement. ## Constructive polynomial approximation in Banach spaces of holomorphic functions Ransford, Thomas | CIRM H Multi angle Research talks Let$X$be a Banach space of holomorphic functions on the unit disk. A linear polynomial approximation scheme for$X$is a sequence of bounded linear operators$T_{n} :X\rightarrow X$with the property that, for each$f\in X$, the functions$T_{n}\left ( f \right )$are polynomials converging to$f$in the norm of the space. We completely characterize those spaces$X$that admit a linear polynomial approximation scheme. In particular, we show that it is not sufficient merely that polynomials be dense in$X$. (Joint work with Javad Mashreghi). Let$X$be a Banach space of holomorphic functions on the unit disk. A linear polynomial approximation scheme for$X$is a sequence of bounded linear operators$T_{n} :X\rightarrow X$with the property that, for each$f\in X$, the functions$T_{n}\left ( f \right )$are polynomials converging to$f$in the norm of the space. We completely characterize those spaces$X$that admit a linear polynomial approximation scheme. In particular, we show ... Déposez votre fichier ici pour le déplacer vers cet enregistrement. ## Norm-preserving extensions of bounded holomorphic functions McCarthy, John | CIRM H Multi angle Research talks Let$V$be an analytic subvariety of a domain$\Omega$in$\mathbb{C}^{n}$. When does$V$have the property that every bounded holomorphic function$f$on$V$has an extension to a bounded holomorphic function on$\Omega$with the same norm? An obvious sufficient condition is if$V$is a holomorphic retract of$\Omega$. We shall discuss for what domains$\Omega$this is also necessary. This is joint work with Łukasz Kosiński. Déposez votre fichier ici pour le déplacer vers cet enregistrement. ## The Szegö minimum problem Borichev, Alexander | CIRM H Multi angle Research talks Given a finite positive measure$\mu$on the unit circle, we consider the distance$e_{n}\left ( \mu \right )$from$z^{n}$to the analytic polynomials of degree less than$n$in$L^{2}\left ( \mu \right )$. We study the asymptotic behavior of$e_{n}\left ( \mu \right )$for$n\rightarrow \infty$when the logarithmic integral of the density of$\mu$diverges for different classes of measures$\mu$. 42C05 Déposez votre fichier ici pour le déplacer vers cet enregistrement. ## Singular rational inner functions on the polydisk Bickel, Kelly | CIRM H Multi angle Research talks This talk will discuss how to study singular rational inner functions (RIFs) using their zero set behaviors. In the two-variable setting, zero sets can be used to define a quantity called contact order, which helps quantify derivative integrability and non-tangential regularity. In the three-variable and higher setting, the RIF singular sets (and corresponding zero sets) can be much more complicated. We will discuss what holds in general, what holds for simple three-variable RIFs, and some examples illustrating why some of the nice two-variable behavior is lost in higher dimensions. This is joint work with James Pascoe and Alan Sola. This talk will discuss how to study singular rational inner functions (RIFs) using their zero set behaviors. In the two-variable setting, zero sets can be used to define a quantity called contact order, which helps quantify derivative integrability and non-tangential regularity. In the three-variable and higher setting, the RIF singular sets (and corresponding zero sets) can be much more complicated. We will discuss what holds in general, ... Déposez votre fichier ici pour le déplacer vers cet enregistrement. ## Closed$G_{2}$-structures Fino, Anna | CIRM H Multi angle Research talks I will review known examples of compact 7-manifolds admitting a closed$G_{2}$-structure. Moreover, I will discuss some results on the behaviour of the Laplacian$G_{2}$-flow starting from a closed$G_{2}\$-structure whose induced metric satisfies suitable extra condition.

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## Finite quantum geometry, exceptional quantum geometry and fundamental particles Dubois-Violette, Michel | CIRM H

Multi angle

Research talks

We show that the spectrum of fundamental particles of matter and their symmetries can be encoded in a finite quantum geometry equipped with a supplementary structure connected with the quark-lepton symmetry. The occurrence of the exceptional quantum geometry for the description of the standard model with 3 generations is suggested. We discuss the field theoretical aspect of this approach taking into account the theory of connections on the corresponding Jordan modules. We show that the spectrum of fundamental particles of matter and their symmetries can be encoded in a finite quantum geometry equipped with a supplementary structure connected with the quark-lepton symmetry. The occurrence of the exceptional quantum geometry for the description of the standard model with 3 generations is suggested. We discuss the field theoretical aspect of this approach taking into account the theory of connections on the ...

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## On the geometry of noncommutative deformations Boucetta, Mohamed | CIRM H

Multi angle

Research talks

53D17

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## Noncommutative localization in smooth Deformation quantization Bordemann, Martin | CIRM H

Multi angle

Research talks

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