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## Post-edited  Zeta functions and monodromy Veys, Wim (Auteur de la Conférence) | CIRM (Editeur )

The $p$-adic Igusa zeta function, topological and motivic zeta function are (related) invariants of a polynomial $f$, reflecting the singularities of the hypersurface $f = 0$. The first one has a number theoretical flavor and is related to counting numbers of solutions of $f = 0$ over finite rings; the other two are more geometric in nature. The monodromy conjecture relates in a mysterious way these invariants to another singularity invariant of $f$, its local monodromy. We will discuss in this survey talk rationality issues for these zeta functions and the origins of the conjecture. The $p$-adic Igusa zeta function, topological and motivic zeta function are (related) invariants of a polynomial $f$, reflecting the singularities of the hypersurface $f = 0$. The first one has a number theoretical flavor and is related to counting numbers of solutions of $f = 0$ over finite rings; the other two are more geometric in nature. The monodromy conjecture relates in a mysterious way these invariants to another singularity invariant of ...

## Post-edited  Wrapping in exact real arithmetic Müller, Norbert (Auteur de la Conférence) | CIRM (Editeur )

A serious problem common to all interval algorithms is that they suffer from wrapping effects, i.e. unnecessary growth of approximations during a computation. This is essentially connected to functional dependencies inside vectors of data computed from the same inputs. Reducing these effects is an important issue in interval arithmetic, where the most successful approach uses Taylor models.
In TTE Taylor models have not been considered explicitly, as they use would not change the induced computability, already established using ordinary interval computations. However for the viewpoint of efficiency, they lead to significant improvements.
In the talk we report on recent improvements on the iRRAM software for exact real arithmetic (ERA) based on Taylor models. The techniques discussed should also easily be applicable to other software for exact real computations as long as they also are based on interval arithmetic.
As instructive examples we consider the one-dimensional logistic map and a few further discrete dynamical systems of higher dimensions
Joint work with Franz Brauße, Trier, and Margarita Korovina, Novosibirsk.
A serious problem common to all interval algorithms is that they suffer from wrapping effects, i.e. unnecessary growth of approximations during a computation. This is essentially connected to functional dependencies inside vectors of data computed from the same inputs. Reducing these effects is an important issue in interval arithmetic, where the most successful approach uses Taylor models.
In TTE Taylor models have not been considered ...

## Post-edited  Whitney problems and real algebraic geometry Fefferman, Charles (Auteur de la Conférence) | CIRM (Editeur )

This talk sketches connections between Whitney problems and e.g. the problem of deciding whether a given rational function on $\mathbb{R}^n$ belongs to $C^m$.

## Post-edited  Which geodesic flows are left-handed? Dehornoy, Pierre (Auteur de la Conférence) | CIRM (Editeur )

Left-handed flows are 3-dimensional flows which have a particular topological property, namely that every pair of periodic orbits is negatively linked. This property (introduced by Ghys in 2007) implies the existence of as many Bikrhoff sections as possible, and therefore allows to reduce the flow to a suspension in many different ways. It then becomes natural to look for examples. A construction of Birkhoff (1917) suggests that geodesic flows are good candidates. In this conference we determine on which hyperbolic orbifolds is the geodesic flow left-handed: the answer is that yes if the surface is a sphere with three cone points, and no otherwise.
dynamical system - geodesic flow - knot - periodic orbit - global section - linking number - fibered knot
Left-handed flows are 3-dimensional flows which have a particular topological property, namely that every pair of periodic orbits is negatively linked. This property (introduced by Ghys in 2007) implies the existence of as many Bikrhoff sections as possible, and therefore allows to reduce the flow to a suspension in many different ways. It then becomes natural to look for examples. A construction of Birkhoff (1917) suggests that geodesic flows ...

## Post-edited  Wall-crossing for Donaldson-Thomas invariants Bridgeland, Tom (Auteur de la Conférence) | CIRM (Editeur )

There is a very general story, due to Joyce and Kontsevich-Soibelman, which associates to a CY3 (three-dimensional Calabi-Yau) triangulated category equipped with a stability condition some rational numbers called Donaldson-Thomas (DT) invariants. The point I want to emphasise is that the wall-crossing formula, which describes how these numbers change as the stability condition is varied, takes the form of an iso-Stokes condition for a family of connections on the punctured disc, where the structure group is the infinite-dimensional group of symplectic automorphisms of an algebraic torus. I will not assume any knowledge of stability conditions, DT invariants etc. There is a very general story, due to Joyce and Kontsevich-Soibelman, which associates to a CY3 (three-dimensional Calabi-Yau) triangulated category equipped with a stability condition some rational numbers called Donaldson-Thomas (DT) invariants. The point I want to emphasise is that the wall-crossing formula, which describes how these numbers change as the stability condition is varied, takes the form of an iso-Stokes condition for a family of ...

## Post-edited  Virtual fundamental cycles and contact homology Pardon, John (Auteur de la Conférence) | CIRM (Editeur )

I will discuss work in progress aimed towards defining contact homology using "virtual" holomorphic curve counting techniques.

## Post-edited  Victor Havin tribute : 50 years with Hardy spaces. What next... ? Nikolski, Nikolai K. (Auteur de la Conférence) | CIRM (Editeur )

Starting with a personal tribute to Victor Havin (1933-2015), I discuss a dozen achievements of Great Havin's Analysis Seminar, as well as some challenging still unsolved problems.
The Havin publications list is available in the PDF file at the bottom of the page.

## Post-edited  Various aspects of the dynamics of the cubic Szegö solutions Grellier, Sandrine (Auteur de la Conférence) | CIRM (Editeur )

The cubic Szegö equation has been introduced as a toy model for totally non dispersive evolution equations. It turned out that it is a complete integrable Hamiltonian system for which we built a non linear Fourier transform giving an explicit expression of the solutions.
This explicit formula allows to study the dynamics of the solutions. We will explain different aspects of it: almost-periodicity of the solutions in the energy space, uniform analyticity for a large set of initial data, turbulence phenomenon for a dense set of smooth initial data in large Sobolev spaces.
From joint works with Patrick Gérard.
The cubic Szegö equation has been introduced as a toy model for totally non dispersive evolution equations. It turned out that it is a complete integrable Hamiltonian system for which we built a non linear Fourier transform giving an explicit expression of the solutions.
This explicit formula allows to study the dynamics of the solutions. We will explain different aspects of it: almost-periodicity of the solutions in the energy space, uniform ...

## Post-edited  Variational formulas, Busemann functions, and fluctuation exponents for the corner growth model with exponential weights - Lecture 1 Seppäläinen, Timo (Auteur de la Conférence) | CIRM (Editeur )

Variational formulas for limit shapes of directed last-passage percolation models. Connections of minimizing cocycles of the variational formulas to geodesics, Busemann functions, and stationary percolation.

## Post-edited  Unresolved problems in the theory of integrable systems Zakharov, Vladimir (Auteur de la Conférence) | CIRM (Editeur )

In spite of enormous success of the theory of integrable systems, at least three important problems are not resolved yet or are resolved only partly. They are the following:
1. The IST in the case of arbitrary bounded initial data.
2. The statistical description of the systems integrable by the IST. Albeit, the development of the theory of integrable turbulence.
3. Integrability of the deep water equations.
These three problems will be discussed in the talk.
In spite of enormous success of the theory of integrable systems, at least three important problems are not resolved yet or are resolved only partly. They are the following:
1. The IST in the case of arbitrary bounded initial data.
2. The statistical description of the systems integrable by the IST. Albeit, the development of the theory of integrable turbulence.
3. Integrability of the deep water equations.
These three problems will be discussed ...

## Post-edited  Unramified graph covers of finite degree Li, Winnie (Auteur de la Conférence) | CIRM (Editeur )

Given a finite connected undirected graph $X$, its fundamental group plays the role of the absolute Galois group of $X$. The familiar Galois theory holds in this setting. In this talk we shall discuss graph theoretical counter parts of several important theorems for number fields. Topics include
(a) Determination, up to equivalence, of unramified normal covers of $X$ of given degree,
(c) Chebotarev density theorem.
This is a joint work with Hau-Wen Huang.
Given a finite connected undirected graph $X$, its fundamental group plays the role of the absolute Galois group of $X$. The familiar Galois theory holds in this setting. In this talk we shall discuss graph theoretical counter parts of several important theorems for number fields. Topics include
(a) Determination, up to equivalence, of unramified normal covers of $X$ of given degree,
(c) Chebotarev density ...

## Post-edited  Unirational varieties - Part 1 Mella, Massimiliano (Auteur de la Conférence) | CIRM (Editeur )

The aim of these talks is to give an overview to unirationality problems. I will discuss the behaviour of unirationality in families and its relation with rational connectedness. Then I will concentrate on hypersurfaces and conic bundles. These special classes of varieties are a good place where to test different techniques and try to approach the unirationality problem via rational connectedness.

## Post-edited  Une deuxième révolution galiléenne ? Dowek, Gilles (Auteur de la Conférence) | CIRM (Editeur )

L'introduction d'un nouveau concept scientifique permet souvent de donner de nouvelles réponses à des questions anciennes qui n'avaient jusqu'alors reçu que des réponses imparfaites. Cet exposé présente quelques questions qui ont trouvé de nouvelles réponses depuis que nous comprenons mieux la notion d'algorithme : qu'est-ce qu'un aéroport ?, qu'est-ce qu'une cellule, qu'est-ce qu'une loi physique ?, ... La prise de conscience du caractère algorithmique de ces objets scientifiques nous amène à considérer de nouveaux langages pour les décrire. Cette révolution, dans le langage dans lequel la science s'écrit, peut-être comparée à la révolution qui s'est produite, au début du XVIIe siècle, quand le langage mathématique a commencé à être utilisé pour décrire des phénomènes physiques. L'introduction d'un nouveau concept scientifique permet souvent de donner de nouvelles réponses à des questions anciennes qui n'avaient jusqu'alors reçu que des réponses imparfaites. Cet exposé présente quelques questions qui ont trouvé de nouvelles réponses depuis que nous comprenons mieux la notion d'algorithme : qu'est-ce qu'un aéroport ?, qu'est-ce qu'une cellule, qu'est-ce qu'une loi physique ?, ... La prise de conscience du caractère ...

## Post-edited  Two-player perfect-information shift-invariant submixing stochastic games are half-positional Gimbert, Hugo (Auteur de la Conférence) | CIRM (Editeur )

We show that two-player stochastic games with perfect-information and shift-invariant submixing payoff functions are half-positional, i.e. in these games the maximizer has a positional optimal strategy. This extension of our previous result for one-player games relies on an interesting existence result about the existence of epsilon-subgame-perfect strategies.

## Post-edited  Totally geodesic submanifolds of Teichmüller space and moduli space Wright, Alexander (Auteur de la Conférence) | CIRM (Editeur )

We consider "higher dimensional Teichmüller discs", by which we mean complex submanifolds of Teichmüller space that contain the Teichmüller disc joining any two of its points. We prove results in the higher dimensional setting that are opposite to the one dimensional behavior: every "higher dimensional Teichmüller disc" covers a "higher dimensional Teichmüller curve" and there are only finitely many "higher dimensional Teichmüller curves" in each moduli space. The proofs use recent results in Teichmüller dynamics, especially joint work with Eskin and Filip on the Kontsevich-Zorich cocycle. Joint work with McMullen and Mukamel as well as Eskin, McMullen and Mukamel shows that exotic examples of "higher dimensional Teichmüller discs" do exist. We consider "higher dimensional Teichmüller discs", by which we mean complex submanifolds of Teichmüller space that contain the Teichmüller disc joining any two of its points. We prove results in the higher dimensional setting that are opposite to the one dimensional behavior: every "higher dimensional Teichmüller disc" covers a "higher dimensional Teichmüller curve" and there are only finitely many "higher dimensional Teichmüller curves" in ...

## Post-edited  Théorie des valeurs extrêmes et problème de sortie stochastique Berglund, Nils (Auteur de la Conférence) | CIRM (Editeur )

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 ...

## Post-edited  The Weil algebra of a Hopf algebra Dubois-Violette, Michel (Auteur de la Conférence) | CIRM (Editeur )

We give a summary of a joint work with Giovanni Landi (Trieste University) on a non commutative generalization of Henri Cartan's theory of operations, algebraic connections and Weil algebra.

## Post-edited  The power of heterogeneous large-scale data for high-dimensional causal inference Bühlmann, Peter (Auteur de la Conférence) | CIRM (Editeur )

We present a novel methodology for causal inference based on an invariance principle. It exploits the advantage of heterogeneity in larger datasets, arising from different experimental conditions (i.e. an aspect of "Big Data"). Despite fundamental identifiability issues, the method comes with statistical confidence statements leading to more reliable results than alternative procedures based on graphical modeling. We also discuss applications in biology, in particular for large-scale gene knock-down experiments in yeast where computational and statistical methods have an interesting potential for prediction and prioritization of new experimental interventions. We present a novel methodology for causal inference based on an invariance principle. It exploits the advantage of heterogeneity in larger datasets, arising from different experimental conditions (i.e. an aspect of "Big Data"). Despite fundamental identifiability issues, the method comes with statistical confidence statements leading to more reliable results than alternative procedures based on graphical modeling. We also discuss applications in ...

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