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Let $p$ be a prime number and $F$ be a non-archimedean field with finite residue class field of characteristic $p$. Understanding the category of Iwahori-Hecke modules for $SL_2(F)$ is of great interest in the study of $p$-modular smooth representations of $SL_2(F)$, as these modules naturally show up as spaces of invariant vectors under the action of the standard pro-$p$-Iwahori subgroup. In this talk, we will discuss a work in progress in which we aim to classify all non-trivial extensions between these modules and to compare them with their analogues for $p$-modular smooth representations of $SL_2(F)$ and with their Galois counterpart in the setting of the local Langlands correspondences in natural characteristic. Let $p$ be a prime number and $F$ be a non-archimedean field with finite residue class field of characteristic $p$. Understanding the category of Iwahori-Hecke modules for $SL_2(F)$ is of great interest in the study of $p$-modular smooth representations of $SL_2(F)$, as these modules naturally show up as spaces of invariant vectors under the action of the standard pro-$p$-Iwahori subgroup. In this talk, we will discuss a work in progress in ...

11F70 ; 11F85 ; 20C08 ; 20G05 ; 22E50

We study the smallest parts function introduced by Andrews. The associated generating function forms a component of a natural mock modular form of weight 3/2 whose shadow is the Dedekind eta function. We obtain an exact formula and an algebraic formula for each value of the smallest parts function; these are analogues of the formulas of Rademacher and Bruinier-Ono for the ordinary partition function. The convergence of our expression is non-trivial; the proof relies on power savings estimates for weighted sums of generalized Kloosterman sums which follow from spectral methods. We study the smallest parts function introduced by Andrews. The associated generating function forms a component of a natural mock modular form of weight 3/2 whose shadow is the Dedekind eta function. We obtain an exact formula and an algebraic formula for each value of the smallest parts function; these are analogues of the formulas of Rademacher and Bruinier-Ono for the ordinary partition function. The convergence of our expression is ...

11F37 ; 11P82

I will describe a recent framework for robust shape reconstruction based on optimal transportation between measures, where the input measurements are seen as distribution of masses. In addition to robustness to defect-laden point sets (hampered with noise and outliers), this approach can reconstruct smooth closed shapes as well as piecewise smooth shapes with boundaries.

68Rxx ; 65D17 ; 65D18

Post-edited  Interview Martin Andler
Andler, Martin (Personne interviewée) | CIRM (Editeur )

Professeur à l'université de Versailles-Saint-Quentin
Président de l'association Animath

Beyond endoscopy is the strategy put forward by Langlands for applying the trace formula to the general principle of functoriality. Subsequent papers by Langlands (one in collaboration with Frenkel and Ngo), together with more recent papers by Altug, have refined the strategy. They all emphasize the importance of understanding the elliptic terms on the geometric side of the trace formula. We shall discuss the general strategy, and how it pertains to these terms. Beyond endoscopy is the strategy put forward by Langlands for applying the trace formula to the general principle of functoriality. Subsequent papers by Langlands (one in collaboration with Frenkel and Ngo), together with more recent papers by Altug, have refined the strategy. They all emphasize the importance of understanding the elliptic terms on the geometric side of the trace formula. We shall discuss the general strategy, and how it ...

11F66 ; 22E50 ; 22E55

Post-edited  Interview at CIRM: Michael Artin
Artin, Michael (Personne interviewée) | CIRM (Editeur )

Michael ARTIN participated in the "Artin Approximation and Infinite dimensional Geometry" event organized at CIRM in March 2015, which was part of the Jean-Morlet semester held by Herwig Hauser. Michael Artin is an American mathematician and a professor emeritus in the Massachusetts Institute of Technology mathematics department, known for his contributions to algebraic geometry and also generally recognized as one of the outstanding professors in his field. Artin was born in Hamburg, Germany, and brought up in Indiana. His parents were Natalia Jasny (Natascha) and Emil Artin, a preeminent algebraist of the 20th century. In 2002, Artin won the American Mathematical Society's annual Steele Prize for Lifetime Achievement. In 2005, he was awarded the Harvard Centennial Medal. He won the Wolf Prize in Mathematics. He is also a member of the National Academy of Sciences and a Fellow of the American Academy of Arts and Sciences, the American Association for the Advancement of Science, the Society for Industrial and Applied Mathematics, and the American Mathematical Society. Michael ARTIN participated in the "Artin Approximation and Infinite dimensional Geometry" event organized at CIRM in March 2015, which was part of the Jean-Morlet semester held by Herwig Hauser. Michael Artin is an American mathematician and a professor emeritus in the Massachusetts Institute of Technology mathematics department, known for his contributions to algebraic geometry and also generally recognized as one of the outstanding professors ...

An oriented manifold possesses an L-homology fundamental class which is an integral refinement of its Hirzebruch L-class and assembles to the symmetric signature. In joint work with Gerd Laures and James McClure, we give a construction of such an L-homology fundamental class for those oriented singular spaces, which are integral intersection homology Poincaré spaces. Our approach constructs a morphism of ad theories from intersection Poincaré bordism to L-theory. We shall indicate an application to the stratified Novikov conjecture. The latter has been treated analytically by Albin, Leichtnam, Mazzeo and Piazza. An oriented manifold possesses an L-homology fundamental class which is an integral refinement of its Hirzebruch L-class and assembles to the symmetric signature. In joint work with Gerd Laures and James McClure, we give a construction of such an L-homology fundamental class for those oriented singular spaces, which are integral intersection homology Poincaré spaces. Our approach constructs a morphism of ad theories from intersection Poincaré ...

55N33 ; 57R67 ; 57R20 ; 57N80 ; 19G24

Dominique Barbolosi est professeur à l'Université d'Aix-Marseille. Après l'agrégation, un doctorat de mathématiques et une longue carrière de chercheur, il est devenu un spécialiste mondialement reconnu dans le domaine des applications des mathématiques à la médecine. Ses recherches actuelles concernent l'utilisation des modèles mathématiques afin d'intégrer la complexité biologique et fournir des outils algorithmiques aux médecins pour optimiser l'efficacité des traitements anticancéreux, tout en limitant leurs effets toxiques. Dominique Barbolosi est professeur à l'Université d'Aix-Marseille. Après l'agrégation, un doctorat de mathématiques et une longue carrière de chercheur, il est devenu un spécialiste mondialement reconnu dans le domaine des applications des mathématiques à la médecine. Ses recherches actuelles concernent l'utilisation des modèles mathématiques afin d'intégrer la complexité biologique et fournir des outils algorithmiques aux médecins pour ...

We prove the consistency and asymptotic normality of the Laplacian Quasi-Maximum Likelihood Estimator (QMLE) for a general class of causal time series including ARMA, AR($\infty$), GARCH, ARCH($\infty$), ARMA-GARCH, APARCH, ARMA-APARCH,..., processes. We notably exhibit the advantages (moment order and robustness) of this estimator compared to the classical Gaussian QMLE. Numerical simulations confirms the accuracy of this estimator.

62F12 ; 62M10

This lecture series will be an introduction to stability conditions on derived categories, wall-crossing, and its applications to birational geometry of moduli spaces of sheaves. I will assume a passing familiarity with derived categories.

- Introduction to stability conditions. I will start with a gentle review of aspects of derived categories. Then an informal introduction to Bridgeland's notion of stability conditions on derived categories [2, 5, 6]. I will then proceed to explain the concept of wall-crossing, both in theory, and in examples [1, 2, 4, 6].

- Wall-crossing and birational geometry. Every moduli space of Bridgeland-stable objects comes equipped with a canonically defined nef line bundle. This systematically explains the connection between wall-crossing and birational geometry of moduli spaces. I will explain and illustrate the underlying construction [7].

- Applications : Moduli spaces of sheaves on $K3$ surfaces. I will explain how one can use the theory explained in the previous talk in order to systematically study the birational geometry of moduli spaces of sheaves, focussing on $K3$ surfaces [1, 8].
This lecture series will be an introduction to stability conditions on derived categories, wall-crossing, and its applications to birational geometry of moduli spaces of sheaves. I will assume a passing familiarity with derived categories.

- Introduction to stability conditions. I will start with a gentle review of aspects of derived categories. Then an informal introduction to Bridgeland's notion of stability conditions on derived categories ...

14D20 ; 14E30 ; 14J28 ; 18E30

We will cover some of the more important results from commutative and noncommutative algebra as far as applications to automatic sequences, pattern avoidance, and related areas. Well give an overview of some applications of these areas to the study of automatic and regular sequences and combinatorics on words.

11B85 ; 68Q45 ; 68R15

Kapustin and Witten introduced a powerful perspective on the geometric Langlands correspondence as an aspect of electric-magnetic duality in four dimensional gauge theory. While the familiar (de Rham) correspondence is best seen as a statement in conformal field theory, much of the structure can be seen in the simpler (Betti) setting of topological field theory using Lurie's proof of the Cobordism Hypothesis. In these lectures I will explain this perspective and illustrate its applications to representation theory following joint work with Nadler as well as Brochier, Gunningham, Jordan and Preygel. Kapustin and Witten introduced a powerful perspective on the geometric Langlands correspondence as an aspect of electric-magnetic duality in four dimensional gauge theory. While the familiar (de Rham) correspondence is best seen as a statement in conformal field theory, much of the structure can be seen in the simpler (Betti) setting of topological field theory using Lurie's proof of the Cobordism Hypothesis. In these lectures I will explain ...

14D24 ; 22E57 ; 22E46 ; 20G05

I shall classify current approaches to multiple inferences according to goals, and discuss the basic approaches being used. I shall then highlight a few challenges that await our attention : some are simple inequalities, others arise in particular applications.

62J15 ; 62P10

In this series of lectures, we will focus on simple Lie groups, their dense subgroups and the convolution powers of their measures. In particular, we will dicuss the following two questions.
Let G be a Lie group. Is every Borel measurable subgroup of G with maximal Hausdorff dimension equal to the group G?
Is the convolution of sufficiently many compactly supported continuous functions on G always continuously differentiable?
Even though the answer to these questions is no when G is abelian, the answer is yes when G is simple. This is a joint work with N. de Saxce. First, I will explain the history of these two questions and their interaction. Then, I will relate these questions to spectral gap properties. Finally, I will discuss these spectral gap properties.
In this series of lectures, we will focus on simple Lie groups, their dense subgroups and the convolution powers of their measures. In particular, we will dicuss the following two questions.
Let G be a Lie group. Is every Borel measurable subgroup of G with maximal Hausdorff dimension equal to the group G?
Is the convolution of sufficiently many compactly supported continuous functions on G always continuously differentiable?
Even though the ...

22E30 ; 28A78 ; 43A65

La théorie des valeurs extrêmes décrit le comportement du maximum d'une suite de variables aléatoires i.i.d. à valeurs réelles. L'une des distributions limites possibles, la loi de Gumbel, apparaît également dans l'asymptotique en bruit faible du temps de transition réactive pour des équations différentielles stochastiques métastables. Nous décrivons des résultats récents en dimension 1 et leur interprétation, et donnons un résultat en dimension 2, motivé par le phénomène de synchronisation d'oscillateurs couplés. La théorie des valeurs extrêmes décrit le comportement du maximum d'une suite de variables aléatoires i.i.d. à valeurs réelles. L'une des distributions limites possibles, la loi de Gumbel, apparaît également dans l'asymptotique en bruit faible du temps de transition réactive pour des équations différentielles stochastiques métastables. Nous décrivons des résultats récents en dimension 1 et leur interprétation, et donnons un résultat en dimension ...

60G70 ; 37H10

This talk is based on a work jointly with Timothy Budd (Copenhagen), Nicolas Curien (Orsay) and Igor Kortchemski (Ecole Polytechnique).
Consider a self-similar Markov process $X$ on $[0,\infty)$ which converges at infinity a.s. We interpret $X(t)$ as the size of a typical cell at time $t$, and each negative jump as a birth event. More precisely, if ${\Delta}X(s) = -y < 0$, then $s$ is the birth at time of a daughter cell with size $y$ which then evolves independently and according to the same dynamics. In turn, daughter cells give birth to granddaughter cells each time they make a negative jump, and so on.
The genealogical structure of the cell population can be described in terms of a branching random walk, and this gives rise to remarkable martingales. We analyze traces of these mar- tingales in physical time, and point at some applications for self-similar growth-fragmentation processes and for planar random maps.
This talk is based on a work jointly with Timothy Budd (Copenhagen), Nicolas Curien (Orsay) and Igor Kortchemski (Ecole Polytechnique).
Consider a self-similar Markov process $X$ on $[0,\infty)$ which converges at infinity a.s. We interpret $X(t)$ as the size of a typical cell at time $t$, and each negative jump as a birth event. More precisely, if ${\Delta}X(s) = -y < 0$, then $s$ is the birth at time of a daughter cell with size $y$ which then ...

60G51 ; 60G18 ; 60J75 ; 60G44 ; 60G50

Post-edited  Interview Gérard Besson
Besson, Gérard (Personne interviewée) | CIRM (Editeur )

Directeur de recherche au CNRS
Institut Fourier - Université de Grenoble 1

Directrice de recherche CNRS au DMA, UMR 8553 (équipe Analyse)
Directrice Adjoint Scientifique à l'Insmi, en charge de la politique de sites (Institut des Sciences Mathématiques et de leurs Interactions - CNRS)
Adjointe Déléguée Scientifique Référente au CNRS

Tous les fournisseurs d'applications mettent actuellement en place des infrastructures "cloud". Cette nouvelle approche de l'utilisation des logiciels va complètement changer notre comportement en tant qu'utilisateurs, mais aussi en tant qu'enseignants et en tant que chercheurs.
L'objectif de cet exposé est de dégager les grands concepts scientifiques de cette évolution technologique et commerciale.
* Pourquoi le cloud aujourd'hui?
* Qu'est-ce qui a permis son émergence si rapide maintenant?
* Qu'est-ce que ça change pour l'enseignement?
* Quels sont les nouveaux défis de recherche qui sont posés?
Tous les fournisseurs d'applications mettent actuellement en place des infrastructures "cloud". Cette nouvelle approche de l'utilisation des logiciels va complètement changer notre comportement en tant qu'utilisateurs, mais aussi en tant qu'enseignants et en tant que chercheurs.
L'objectif de cet exposé est de dégager les grands concepts scientifiques de cette évolution technologique et commerciale.
* Pourquoi le cloud aujourd'hui?
* Qu'est-ce ...

68Qxx

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