### Modèles Bayésiens non paramétriques pour l'analyse de données

Guillaume Kon Kam King
​L'intérêt pour l'intelligence artificielle (IA) s'est considérablement accru ces dernières années et l'IA a été appliquée avec succès à des problèmes de société. Le Big Data, le recueil et l’analyse des données, la statistique se penchent sur l’amélioration de la société de demain. Big Data en santé publique, dans le domaine de la justice pénale, de la sécurité aéroportuaire, des changements climatiques, de la protection des espèces en voie de disparition, etc. ​ ​C'est sur...

### Morsifications and mutations

Sergey Fomin
I will discuss a connection between the topology of isolated singularities of plane curves and the mutation equivalence of the quivers associated with their morsifications. Joint work with Pavlo Pylyavskyy, Eugenii Shustin, and Dylan Thurston.

### Quantum $\mathfrak{sl}_n$ knot cohomology and the slice genus

Andrew Lobb
We will give an overview of the information about the smooth slice genus so far yielded by the quantum $\mathfrak{sl}_n$ knot cohomologies.

### Variational and non-Archimedean aspects of the Yau-Tian-Donaldson conjecture

Sébastien Boucksom
I will discuss some recent developments in the direction of the Yau-Tian-Donaldson conjecture, which relates the existence of constant scalar curvature Kähler metrics to the algebro-geometric notion of $K$-stability. The emphasis will be put on the use of pluripotential theory and the interpretation of $K$-stability in terms of non-Archimedean geometry.

### L-space knots in twist families and satellite L-space knots

Kimihiko Motegi
Twisting a knot $K$ in $S^3$ along a disjoint unknot $c$ produces a twist family of knots $\{K_n\}$ indexed by the integers. Comparing the behaviors of the Seifert genus $g(K_n)$ and the slice genus $g_4(K_n)$ under twistings, we prove that if $g(K_n) - g_4(K_n) < C$ for some constant $C$ for infinitely many integers $n > 0$ or $g(K_n) / g_4(K_n) \to 1$ as $n \to \infty$, then either the winding number of $K$ about...

### Automorphy lifting via level lowering congruences

Chandrashekhar Khare

### Deformation theory of twistor spaces of K3 surfaces​

Ana-Maria Brecan
Twistor spaces of K3 surfaces are non-Kähler compact complex manifolds which play a fundamental role in the moduli theory of K3 surfaces. They come equipped with a holomorphic submersion to the complex projective line which under the period map corresponds to a twistor line in the K3-period domain. In this talk I will explain how one can view a twistor line as a certain base point in the linear cycle space of the period domain....

### Extremal Poincaré type metrics and stability of pairs on Hirzebruch surfaces

Lars Martin Sektnan
In this talk I will discuss the existence of complete extremal metrics on the complement of simple normal crossings divisors in compact Kähler manifolds, and stability of pairs, in the toric case. Using constructions of Legendre and Apostolov-Calderbank-Gauduchon, we completely characterize when this holds for Hirzebruch surfaces. In particular, our results show that relative stability of a pair and the existence of extremal Poincaré type/cusp metrics do not coincide. However, stability is equivalent to the...

### Large-time behavior in (hypo)coercive ODE-systems and kinetic models

Anton Arnold
In this talk we discuss the convergence to equilibrium in conservative-dissipative ODE-systems, kinetic relaxation models (of BGK-type), and Fokker-Planck equation. This will include symmetric, non-symmetric and hypocoercive evolution equations. A main focus will be on deriving sharp decay rates. We shall start with hypocoercivity in ODE systems, with the ”hypocoercivity index” characterizing its structural complexity. BGK equations are kinetic transport equations with a relaxation operator that drives the phase space distribution towards the spatially local...

### Equidistribution of square-tiled surfaces, meanders, and Masur-Veech volumes

Anton Zorich
We show how recent results of the authors on equidistribution of square-tiled surfaces of given combinatorial type allow to compute approximate values of Masur-Veech volumes of the strata in the moduli spaces of Abelian and quadratic differentials by Monte Carlo method. We also show how similar approach allows to count asymptotical number of meanders of fixed combinatorial type in various settings in all genera. Our formulae are particularly efficient for classical meanders in genus zero....

### Structures de données complexes et traitement de données massives

Christian Lenne
Proposition d'une démarche pour le traitement de données complexes et/ou massives à des fins d'exploration interactive. Basée sur la mise en œuvre effective dans un contexte de données de santé, cette démarche propose d'explorer des notions connues mais peu utilisées qui émergent comme les bases graphes pour modéliser un lac de données et l'exploiter. Nous balayons quelques environnements système (Hadoop, bases NoSQL, ETL) et effleurons les contraintes de sécurité d'accès.

### Trisections diagrams and surgery operations on embedded surfaces​

David Gay
Various surgery operations on dimension four begin with a 4–manifold $X$ and an embedded surface $S$, then remove a neighborhood of $S$ and replace it with something else to produce an interesting new 4–manifold. In a few standard surgery constructions, especially the Gluck twist operation, I will show how, given a trisection diagram of $X$ with decorations that describe the embedded surface $S$, to produce a trisection diagram for the new 4–manifold. This is joint...

### Simultaneous rational approximations to several functions of a real variable

Victor Beresnevich
As is well known, simultaneous rational approximations to the values of smooth functions of real variables involve counting and/or understanding the distribution of rational points lying near the manifold parameterised by these functions. I will discuss recent results in this area regarding lower bounds for the Hausdorff dimension of $\tau$-approximable values, where $\tau\geq \geq 1/n$ is the exponent of approximations. In particular, I will describe a very recent development for non-degenerate maps as well as...

### Inference for spatio-temporal changes of arctic sea ice

Noel A. C. Cressie
Arctic sea-ice extent has been of considerable interest to scientists in recent years, mainly due to its decreasing trend over the past 20 years. In this talk, I propose a hierarchical spatio-temporal generalized linear model (GLM) for binary Arctic-sea-ice data, where data dependencies are introduced through a latent, dynamic, spatio-temporal mixed-effects model. By using a fixed number of spatial basis functions, the resulting model achieves both dimension reduction and non-stationarity for spatial fields at different...

### Introduction aux technologies et applications Big Data

Sylvain Allemand
Depuis les années 2000, l'informatique a vu émerger de nouvelles technologies, cloud et big data, qui bouleversent l'industrie avec l'arrivée d'outils de traitement à grande échelle. De nouveaux besoins sont apparus comme la possibilité d'extraire de la valeur des données en s'appuyant sur des outils qui répondent aux nouvelles exigences technologiques. Les architectures distribuées comme Hadoop, les bases de données non-relationnelles, les traitements parallélisés avec MapReduce constituent des outils qui répondent aux accroissements massifs des...

### Interview au CIRM : Michel Broué

Michel Broué
Michel Broué travaille en théorie des représentations et se considère comme un "algébriste". Sa thèse de 3ème cycle et sa thèse d'État ont été préparées et soutenues sous la direction de Claude Chevalley et partiellement de Jean-Pierre Serre. Il a fondé et dirigé le "Département de mathématiques et d'informatique" de l'École normale supérieure de Paris, puis dirigé l'Institut Henri-Poincaré, et a été membre senior de l'Institut Universitaire de France. "Foreign honorary member" de l'American Academy...

### An introduction to particle filters

Nicolas Chopin
This course will give a gentle introduction to SMC (Sequential Monte Carlo algorithms): • motivation: state-space (hidden Markov) models, sequential analysis of such models; non-sequential problems that may be tackled using SMC. • Formalism: Markov kernels, Feynman-Kac distributions. • Monte Carlo tricks: importance sampling and resampling • standard particle filters: bootstrap, guided, auxiliary • maximum likelihood estimation of state-stace models • Bayesian estimation of these models: PMCMC, SMC$^2$.

### Signal processing for nonlinear diffractive imaging

Ulugbek Kamilov
Can modern signal processing be used to overcome the diffraction limit? The classical diffraction limit states that the resolution of a linear imaging system is fundamentally limited by one half of the wavelength of light. This implies that conventional light microscopes cannot distinguish two objects placed within a distance closer than 0.5 × 400 = 200nm (blue) or 0.5 × 700 = 350nm (red). This significantly impedes biomedical discovery by restricting our ability to observe...

### An introduction to the BV-BFV formalism

Alberto S. Cattaneo
The BV-BFV formalism unifies the BV formalism (which deals with the problem of fixing the gauge of field theories on closed manifolds) with the BFV formalism (which yields a cohomological resolution of the reduced phase space of a classical field theory). I will explain how this formalism arises and how it can be quantized.

### Automorphisms of hyperbolic groups and growth

Camille Horbez
Let $G$ be a torsion-free hyperbolic group, let $S$ be a finite generating set of $G$, and let $f$ be an automorphism of $G$. We want to understand the possible growth types for the word length of $f^n(g)$, where $g$ is an element of $G$. Growth was completely described by Thurston when $G$ is the fundamental group of a hyperbolic surface, and can be understood from Bestvina-Handel's work on train-tracks when $G$ is a free...

### Homogeneous vector bundles over abelian varieties

Michel Brion
The objects of the talk are the translation-invariant vector bundles over an abelian variety. We will present a representation-theoretic description of these vector bundles, which displays a remarkable analogy with finite-dimensional representations of a compact connected Lie group: the weight lattice is replaced with the dual abelian variety, the Weyl group with the Galois group of the ground field...

### ​On the motive of the stack of vector bundles on a curve

Victoria Hoskins
Following Grothendieck’s vision that a motive of an algebraic variety should capture many of its cohomological invariants, Voevodsky introduced a triangulated category of motives which partially realises this idea. After describing some of the properties of this category, I explain how to define the motive of certain algebraic stacks. I will then focus on defining and studying the motive of the moduli stack of vector bundles on a smooth projective curve and show that this...

### Bridge trisections of knotted surfaces in four-manifolds​

Jeffrey Meier
In this talk, we will develop the theory of generalized bridge trisections for smoothly embedded closed surfaces in smooth, closed four-manifolds. The main result is that any such surface can be isotoped to lie in bridge trisected position with respect to a given trisection of the ambient four-manifold. In the setting of knotted surfaces in the four-sphere, this gives a diagrammatic calculus that offers a promising new approach to four-dimensional knot theory. However, the theory...

### Stochastic solutions of 2D fluids​

Franco Flandoli
We revise recent contributions to 2D Euler and Navier-Stokes equations with and without noise, but always in the case of stochastic solutions. The role of white noise initial conditions will be stressed and related to some questions about turbulence.

### Discounting invariant FTAP for large financial markets

Daniel Balint
For large financial markets as introduced in Kramkov and Kabanov 94, there are several existing absence-of-arbitrage conditions in the literature. They all have in common that they depend in a crucial way on the discounting factor. We introduce a new concept, generalizing NAA1 (K&K 94) and NAA (Rokhlin 08), which is invariant with respect to discounting. We derive a dual characterization by a contiguity property (FTAP).We investigate connections to the in finite time horizon framework...

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