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Documents : Multi angle  Conférences Vidéo | enregistrements trouvés : 200

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In the way of Arnoux-Ito, we give a general geometric criterion for a subshift to be measurably conjugated to a domain exchange and to a translation on a torus. For a subshift coming from an unit Pisot irreducible substitution, we will see that it becomes a simple topological criterion. More precisely, we define a topology on $\mathbb{Z}^d$ for which the subshift has pure discrete spectrum if and only if there exists a domain of the domain exchange on the discrete line that has non-empty interior. We will see how we can compute exactly such interior using regular languages. This gives a way to decide the Pisot conjecture for any example of unit Pisot irreducible substitution.
Joint work with Shigeki Akiyama.
In the way of Arnoux-Ito, we give a general geometric criterion for a subshift to be measurably conjugated to a domain exchange and to a translation on a torus. For a subshift coming from an unit Pisot irreducible substitution, we will see that it becomes a simple topological criterion. More precisely, we define a topology on $\mathbb{Z}^d$ for which the subshift has pure discrete spectrum if and only if there exists a domain of the domain ...

37B10 ; 28A80 ; 11A63 ; 68R15

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Multi angle  Where maths meet cancer
Chomienne, Christine (Auteur de la Conférence) | CIRM (Editeur )

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Cournot Centre session devoted to the transformations that took place in mathematical economics during the interwar period.

01A60 ; 62P20 ; 91BXX

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We provide a general framework to study viability and arbitrage in models for financial markets. Viability is intended as the existence of a preference relation with the following properties: It is consistent with a set of preferences representing all the plausible agents trading in the market; An agent with such a preference is in equilibrium, namely, he or she prefers to stay at the initial endowment respect to trade. We extend the original framework of Kreps ('79) and Harrison-Kreps ('79) to accommodate for Knightian Uncertainty: preferences of plausible agents are not necessarily determined by a single probability measure. The relations between arbitrage, viability, and existence of (non-)linear pricing rules are investigated.
This is a joint work with Frank Riedel and Mete Soner.
We provide a general framework to study viability and arbitrage in models for financial markets. Viability is intended as the existence of a preference relation with the following properties: It is consistent with a set of preferences representing all the plausible agents trading in the market; An agent with such a preference is in equilibrium, namely, he or she prefers to stay at the initial endowment respect to trade. We extend the original ...

91B02 ; 91B52 ; 60H30

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Plans de gestion des données (DMP)
OPIDoR (DMP OPIdoR, Cat opidOr, Datacite) et Doranum.

68M11 ; 68P05

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I will discuss a joint work with Jose Canizo, Cao Chuqi and Havva Yolda. I will introduce Harris’s theorem which is a classical theorem from the study of Markov Processes. Then I will discuss how to use this to show convergence to equilibrium for some spatially inhomogeneous kinetic equations involving jumps including jump processes which approximate diffusion or fractional diffusion in velocity. This is the situation in which the tools of ’Hypocoercivity’ are used. I will discuss the connections to hypocoercivity theory and possible advantages and disadvantages of approaches via Harris’s theorem.
I will discuss a joint work with Jose Canizo, Cao Chuqi and Havva Yolda. I will introduce Harris’s theorem which is a classical theorem from the study of Markov Processes. Then I will discuss how to use this to show convergence to equilibrium for some spatially inhomogeneous kinetic equations involving jumps including jump processes which approximate diffusion or fractional diffusion in velocity. This is the situation in which the tools of ...

35Q20 ; 35B40 ; 60J75 ; 82C40

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The classical Tverberg's theorem says that a set with sufficiently many points in $R^d$ can always be partitioned into m parts so that the (m - 1)-simplex is the (nerve) intersection pattern of the convex hulls of the parts. Our main results demonstrate that Tverberg's theorem is but a special case of a much more general situation. Given sufficiently many points, any tree or cycle, can also be induced by at least one partition of the point set. The proofs require a deep investigation of oriented matroids and order types.
(Joint work with Deborah Oliveros, Tommy Hogan, Dominic Yang (supported by NSF).)
The classical Tverberg's theorem says that a set with sufficiently many points in $R^d$ can always be partitioned into m parts so that the (m - 1)-simplex is the (nerve) intersection pattern of the convex hulls of the parts. Our main results demonstrate that Tverberg's theorem is but a special case of a much more general situation. Given sufficiently many points, any tree or cycle, can also be induced by at least one partition of the point set. ...

05B35 ; 52C40

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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 work with Jeff Meier.
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 ...

57M50 ; 57R45 ; 57R65 ; 57R17

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Multi angle  Tracing the dark matter web
Shandarin, Sergei (Auteur de la Conférence) | CIRM (Editeur )

Dark matter (DM) constitutes almost 85% of all mass able to cluster into gravitationally bound objects. Thus it has played the determining role in the origin and evolution of the structure in the universe often referred to as the Cosmic Web. The dark matter component of the Cosmic Web or simply the Dark Matter Web is considerably easier to understand theoretically than the baryonic component of the web if one assumes that DM interacts only gravitationally. One of the major differences between the DM and baryonic webs consists in the multi stream structure of the DM web. Thus it allows to use three diagnostic fields that do not present in the baryonic web: the number of streams field in Eulerian space, the number of flip flops field in Lagrangian space, and the caustic structure in the both. Although these characteristics have been known for a long time their systematic studies as fields started only a few years ago. I will report new recent results of numerical studies of the three fields mentioned above and also discuss the features of the DM web they have unveil.
Dark matter (DM) constitutes almost 85% of all mass able to cluster into gravitationally bound objects. Thus it has played the determining role in the origin and evolution of the structure in the universe often referred to as the Cosmic Web. The dark matter component of the Cosmic Web or simply the Dark Matter Web is considerably easier to understand theoretically than the baryonic component of the web if one assumes that DM interacts only ...

85A15 ; 85A25 ; 85A40 ; 83F05

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Aim of the lecture is to give an introduction to $K3$ surfaces, that are special algebraic surfaces with an extremely rich geometry. The most easy example of such a surface is the Fermat quartic in complex three-dimensional space.
The name $K3$ was given by André Weil in 1958 in honour of the three remarkable mathematicians: Kummer, Kähler and Kodaira and of the beautiful K2 mountain at Cachemire.
The topics of the lecture are the following:

* $K3$ surfaces in the Enriques-Kodaira classification.
* Examples; Kummer surfaces.
* Basic properties of $K3$ surfaces; Torelli theorem and surjectivity of the period map.
* The study of automorphisms on $K3$ surfaces: basic facts, examples.
* Symplectic automorphisms of $K3$ surfaces, classification, moduli spaces.
Aim of the lecture is to give an introduction to $K3$ surfaces, that are special algebraic surfaces with an extremely rich geometry. The most easy example of such a surface is the Fermat quartic in complex three-dimensional space.
The name $K3$ was given by André Weil in 1958 in honour of the three remarkable mathematicians: Kummer, Kähler and Kodaira and of the beautiful K2 mountain at Cachemire.
The topics of the lecture are the following:

* ...

14J10 ; 14J28 ; 14J50 ; 14C20 ; 14C22 ; 14J27 ; 14L30

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Aim of the lecture is to give an introduction to $K3$ surfaces, that are special algebraic surfaces with an extremely rich geometry. The most easy example of such a surface is the Fermat quartic in complex three-dimensional space.
The name $K3$ was given by André Weil in 1958 in honour of the three remarkable mathematicians: Kummer, Kähler and Kodaira and of the beautiful K2 mountain at Cachemire.
The topics of the lecture are the following:

* $K3$ surfaces in the Enriques-Kodaira classification.
* Examples; Kummer surfaces.
* Basic properties of $K3$ surfaces; Torelli theorem and surjectivity of the period map.
* The study of automorphisms on $K3$ surfaces: basic facts, examples.
* Symplectic automorphisms of $K3$ surfaces, classification, moduli spaces.
Aim of the lecture is to give an introduction to $K3$ surfaces, that are special algebraic surfaces with an extremely rich geometry. The most easy example of such a surface is the Fermat quartic in complex three-dimensional space.
The name $K3$ was given by André Weil in 1958 in honour of the three remarkable mathematicians: Kummer, Kähler and Kodaira and of the beautiful K2 mountain at Cachemire.
The topics of the lecture are the following:

* ...

14J10 ; 14J28 ; 14J50 ; 14C20 ; 14C22 ; 14J27 ; 14L30

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Aim of the lecture is to give an introduction to $K3$ surfaces, that are special algebraic surfaces with an extremely rich geometry. The most easy example of such a surface is the Fermat quartic in complex three-dimensional space.
The name $K3$ was given by André Weil in 1958 in honour of the three remarkable mathematicians: Kummer, Kähler and Kodaira and of the beautiful K2 mountain at Cachemire.
The topics of the lecture are the following:

* $K3$ surfaces in the Enriques-Kodaira classification.
* Examples; Kummer surfaces.
* Basic properties of $K3$ surfaces; Torelli theorem and surjectivity of the period map.
* The study of automorphisms on $K3$ surfaces: basic facts, examples.
* Symplectic automorphisms of $K3$ surfaces, classification, moduli spaces.
Aim of the lecture is to give an introduction to $K3$ surfaces, that are special algebraic surfaces with an extremely rich geometry. The most easy example of such a surface is the Fermat quartic in complex three-dimensional space.
The name $K3$ was given by André Weil in 1958 in honour of the three remarkable mathematicians: Kummer, Kähler and Kodaira and of the beautiful K2 mountain at Cachemire.
The topics of the lecture are the following:

* ...

14J10 ; 14J28 ; 14J50 ; 14C20 ; 14C22 ; 14J27 ; 14L30

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Aim of the lecture is to give an introduction to $K3$ surfaces, that are special algebraic surfaces with an extremely rich geometry. The most easy example of such a surface is the Fermat quartic in complex three-dimensional space.
The name $K3$ was given by André Weil in 1958 in honour of the three remarkable mathematicians: Kummer, Kähler and Kodaira and of the beautiful K2 mountain at Cachemire.
The topics of the lecture are the following:

* $K3$ surfaces in the Enriques-Kodaira classification.
* Examples; Kummer surfaces.
* Basic properties of $K3$ surfaces; Torelli theorem and surjectivity of the period map.
* The study of automorphisms on $K3$ surfaces: basic facts, examples.
* Symplectic automorphisms of $K3$ surfaces, classification, moduli spaces.
Aim of the lecture is to give an introduction to $K3$ surfaces, that are special algebraic surfaces with an extremely rich geometry. The most easy example of such a surface is the Fermat quartic in complex three-dimensional space.
The name $K3$ was given by André Weil in 1958 in honour of the three remarkable mathematicians: Kummer, Kähler and Kodaira and of the beautiful K2 mountain at Cachemire.
The topics of the lecture are the following:

* ...

14J10 ; 14J28 ; 14J50 ; 14C20 ; 14C22 ; 14J27 ; 14L30

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Aim of the lecture is to give an introduction to $K3$ surfaces, that are special algebraic surfaces with an extremely rich geometry. The most easy example of such a surface is the Fermat quartic in complex three-dimensional space.
The name $K3$ was given by André Weil in 1958 in honour of the three remarkable mathematicians: Kummer, Kähler and Kodaira and of the beautiful K2 mountain at Cachemire.
The topics of the lecture are the following:

* $K3$ surfaces in the Enriques-Kodaira classification.
* Examples; Kummer surfaces.
* Basic properties of $K3$ surfaces; Torelli theorem and surjectivity of the period map.
* The study of automorphisms on $K3$ surfaces: basic facts, examples.
* Symplectic automorphisms of $K3$ surfaces, classification, moduli spaces.
Aim of the lecture is to give an introduction to $K3$ surfaces, that are special algebraic surfaces with an extremely rich geometry. The most easy example of such a surface is the Fermat quartic in complex three-dimensional space.
The name $K3$ was given by André Weil in 1958 in honour of the three remarkable mathematicians: Kummer, Kähler and Kodaira and of the beautiful K2 mountain at Cachemire.
The topics of the lecture are the following:

* ...

14J10 ; 14J28 ; 14J50 ; 14C20 ; 14C22 ; 14J27 ; 14L30

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The weak-$A_\infty$ condition is a variant of the usual $A_\infty$ condition which does not require any doubling assumption on the weights. A few years ago Hofmann and Le showed that, for an open set $\Omega\subset \mathbb{R}^{n+1}$ with $n$-AD-regular boundary, the BMO-solvability of the Dirichlet problem for the Laplace equation is equivalent to the fact that the harmonic measure satisfies the weak-$A_\infty$ condition. Aiming for a geometric description of the open sets whose associated harmonic measure satisfies the weak-$A_\infty$ condition, Hofmann and Martell showed in 2017 that if $\partial\Omega$ is uniformly $n$-rectifiable and a suitable connectivity condition holds (the so-called weak local John condition), then the harmonic measure satisfies the weak-$A_\infty$ condition, and they conjectured that the converse implication also holds.
In this talk I will discuss a recent work by Azzam, Mourgoglou and myself which completes the proof of the Hofman-Martell conjecture, by showing that the weak-$A_\infty$ condition for harmonic measure implies the weak local John condition.
The weak-$A_\infty$ condition is a variant of the usual $A_\infty$ condition which does not require any doubling assumption on the weights. A few years ago Hofmann and Le showed that, for an open set $\Omega\subset \mathbb{R}^{n+1}$ with $n$-AD-regular boundary, the BMO-solvability of the Dirichlet problem for the Laplace equation is equivalent to the fact that the harmonic measure satisfies the weak-$A_\infty$ condition. Aiming for a geometric ...

31B15 ; 28A75 ; 28A78 ; 35J15 ; 35J08

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One of the most fundamental problem in tiling theory is to decide, given a surface, a set of tiles and a tiling rule, whether there exist a way to tile the surface using the set of tiles and following the rules. As proven by Berger in the 60’s, this problem is undecidable in general.
When formulated in terms of tilings of the discrete plane by unit tiles with colored constraints, this is called the Domino Problem and was introduced by Wang in an effort to solve satisfaction problems for ??? formulas by translating the problem into a geometric problem.
In this course, we will give a brief description of the problem and to the meaning of the word “undecidable”, and then give two different proofs of the result.
One of the most fundamental problem in tiling theory is to decide, given a surface, a set of tiles and a tiling rule, whether there exist a way to tile the surface using the set of tiles and following the rules. As proven by Berger in the 60’s, this problem is undecidable in general.
When formulated in terms of tilings of the discrete plane by unit tiles with colored constraints, this is called the Domino Problem and was introduced by Wang in an ...

03D35 ; 05B45

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Multi angle  The quantum Vlasov equation
Mauser, Norbert (Auteur de la Conférence) | CIRM (Editeur )

We present the Quantum Vlasov or Wigner equation as a "phase space" presentation of quantum mechanics that is close to the classical Vlasov equation, but where the "distribution function" $w(x,v,t)$ will in general have also negative values.
We discuss the relation to the classical Vlasov equation in the semi-classical asymptotics of small Planck's constant, for the linear case [2] and for the nonlinear case where we couple the quantum Vlasov equation to the Poisson equation [4, 3, 5] and [1].
Recently, in some sort of "inverse semiclassical limit" the numerical concept of solving Schrödinger-Poisson as an approximation of Vlasov-Poisson attracted attention in cosmology, which opens a link to the "smoothed Schrödinger/Wigner numerics" of Athanassoulis et al. (e.g. [6]).
We present the Quantum Vlasov or Wigner equation as a "phase space" presentation of quantum mechanics that is close to the classical Vlasov equation, but where the "distribution function" $w(x,v,t)$ will in general have also negative values.
We discuss the relation to the classical Vlasov equation in the semi-classical asymptotics of small Planck's constant, for the linear case [2] and for the nonlinear case where we couple the quantum Vlasov ...

35Q40 ; 35J10 ; 81Q20 ; 81S30

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In this talk I will explain recent joint work with Rafe Mazzeo, Hartmut Weiss and Frederik Witt on the asymptotics of the natural $L^2$-metric $G_{L^2}$ on the moduli space $\mathcal{M}$ of rank-2 Higgs bundles over a Riemann surface $\Sigma$ as given by the set of solutions to the so-called self-duality equations
$\begin{cases}
&0 = \bar{\partial}_A \Phi \\
& 0 = F_A + [ \Phi \wedge \Phi^*]
\end{cases}$
for a unitary connection $A$ and a Higgs field $\Phi$ on $\Sigma$. I will show that on the regular part of the Hitchin fibration ($A$, $\Phi$) $\rightarrow$ det $\Phi$ this metric is well-approximated by the semiflat metric $G_{sf}$ coming from the completely integrable system on $\mathcal{M}$. This also reveals the asymptotically conic structure of $G_{L^2}$, with (generic) fibres of the above fibration being asymptotically flat tori. This result confirms some aspects of a more general conjectural picture made by Gaiotto, Moore and Neitzke. Its proof is based on a detailed understanding of the ends structure of $\mathcal{M}$. The analytic methods used there in addition yield a complete asymptotic expansion of the difference $G_{L^2} − G_{sf}$ between the two metrics.
In this talk I will explain recent joint work with Rafe Mazzeo, Hartmut Weiss and Frederik Witt on the asymptotics of the natural $L^2$-metric $G_{L^2}$ on the moduli space $\mathcal{M}$ of rank-2 Higgs bundles over a Riemann surface $\Sigma$ as given by the set of solutions to the so-called self-duality equations
$\begin{cases}
&0 = \bar{\partial}_A \Phi \\
& 0 = F_A + [ \Phi \wedge \Phi^*]
\end{cases}$
for a unitary connection $A$ and a ...

53C07 ; 53C26 ; 53D18 ; 14H60 ; 14D20

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The Farrell-Jones conjecture for a given group is an important conjecture in manifold theory. I will review some of its consequences and will discuss a class of groups for which it is known, for example 3-manifold groups. Finally, I will discuss a proof that free-by-cyclic groups satisfy FJC, answering a question of Lück.
This is joint work with Koji Fujiwara and Derrick Wigglesworth.

57M20 ; 20F65 ; 57M07 ; 18F25

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