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Documents : Virtualconference  | enregistrements trouvés : 192

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Algebraic combinatorics studies combinatorial objects with an algebraic point of view, and conversely. As such, it is also a very fertile ground for experimental mathematics, involving both classical and new algorithms. I will discuss two topics: finite partially ordered sets and their invariants, and tree-indexed polynomials and power series. Finite partially ordered sets are discrete objects, that can be seen as directed graphs, but also possess an interesting representation theory. This leads to many difficult questions about a subtle equivalence relation, namely posets having equivalent derived categories. The theme of tree-indexed series, which can be traced back to Cayley, plays a role in the study of vector fields and ordinary differential equations. It is nowadays better understood in the framework of operads and can be considered as a nonassociative version of the study of alphabets, words and languages. Surprisingly maybe, rooted trees also appear in the study of iterated integrals, stemming out of the usual "integration-by-part" rule. I will describe the corresponding notions of algebras, without diving too much into the theory of operads. On the way, I will discuss some of the involved algorithms and their implementations.
Algebraic combinatorics studies combinatorial objects with an algebraic point of view, and conversely. As such, it is also a very fertile ground for experimental mathematics, involving both classical and new algorithms. I will discuss two topics: finite partially ordered sets and their invariants, and tree-indexed polynomials and power series. Finite partially ordered sets are discrete objects, that can be seen as directed graphs, but also ...

06A06 ; 17A30 ; 18G80 ; 16G20

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Robotic design involves modeling the behavior of a robot mechanism when it moves along potential paths set by the users. In this lecture, we will first give an overview of different approaches to design a set of kinematic equations associated with a robot mechanism. In particular, these equations can be used to solve the forward and the backward kinematics problems associated with a robot mechanism or to model its singularity locus. Then we will review methods to solve those equations, and notably methods to draw with guarantees the real solutions of an under-constrained system of equations modeling the singularities of a robot.
Robotic design involves modeling the behavior of a robot mechanism when it moves along potential paths set by the users. In this lecture, we will first give an overview of different approaches to design a set of kinematic equations associated with a robot mechanism. In particular, these equations can be used to solve the forward and the backward kinematics problems associated with a robot mechanism or to model its singularity locus. Then we will ...

68T01 ; 65G20 ; 68W30 ; 65Dxx

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Algebraic combinatorics studies combinatorial objects with an algebraic point of view, and conversely. As such, it is also a very fertile ground for experimental mathematics, involving both classical and new algorithms. I will discuss two topics: finite partially ordered sets and their invariants, and tree-indexed polynomials and power series. Finite partially ordered sets are discrete objects, that can be seen as directed graphs, but also possess an interesting representation theory. This leads to many difficult questions about a subtle equivalence relation, namely posets having equivalent derived categories. The theme of tree-indexed series, which can be traced back to Cayley, plays a role in the study of vector fields and ordinary differential equations. It is nowadays better understood in the framework of operads and can be considered as a nonassociative version of the study of alphabets, words and languages. Surprisingly maybe, rooted trees also appear in the study of iterated integrals, stemming out of the usual "integration-by-part" rule. I will describe the corresponding notions of algebras, without diving too much into the theory of operads. On the way, I will discuss some of the involved algorithms and their implementations.
Algebraic combinatorics studies combinatorial objects with an algebraic point of view, and conversely. As such, it is also a very fertile ground for experimental mathematics, involving both classical and new algorithms. I will discuss two topics: finite partially ordered sets and their invariants, and tree-indexed polynomials and power series. Finite partially ordered sets are discrete objects, that can be seen as directed graphs, but also ...

06A06 ; 16G20 ; 17A30 ; 18G80

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Robotic design involves modeling the behavior of a robot mechanism when it moves along potential paths set by the users. In this lecture, we will first give an overview of different approaches to design a set of kinematic equations associated with a robot mechanism. In particular, these equations can be used to solve the forward and the backward kinematics problems associated with a robot mechanism or to model its singularity locus. Then we will review methods to solve those equations, and notably methods to draw with guarantees the real solutions of an under-constrained system of equations modeling the singularities of a robot.
Robotic design involves modeling the behavior of a robot mechanism when it moves along potential paths set by the users. In this lecture, we will first give an overview of different approaches to design a set of kinematic equations associated with a robot mechanism. In particular, these equations can be used to solve the forward and the backward kinematics problems associated with a robot mechanism or to model its singularity locus. Then we will ...

68T40 ; 65G20 ; 68W30 ; 65Dxx

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This talk will give an overview on the usage of piecewise deterministic Markov processes for risk theoretic modeling and the application of QMC integration in this framework. This class of processes includes several common risk models and their generalizations. In this field, many objects of interest such as ruin probabilities, penalty functions or expected dividend payments are typically studied by means of associated integro-differential equations. Unfortunately, only particular parameter constellations allow for closed form solutions such that in general one needs to rely on numerical methods. Instead of studying these associated integro-differential equations, we adapt the problem in a way that allows us to apply deterministic numerical integration algorithms such as QMC rules.
This talk will give an overview on the usage of piecewise deterministic Markov processes for risk theoretic modeling and the application of QMC integration in this framework. This class of processes includes several common risk models and their generalizations. In this field, many objects of interest such as ruin probabilities, penalty functions or expected dividend payments are typically studied by means of associated integro-differential ...

91B30 ; 91G60 ; 60J25 ; 65R20

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Estimation of conditional quantiles is requiered for many purposes, in particular when the conditional mean is not suffisiant to describe the impact of covariates on the dependent variable. For example, one may estimate the quantile of one financial index (e.g. WisdomTree Japan Hedged Equity Fund) knowing financial indeces from other countries. It is also requiered to estimated conditional quantiles in Quantile Oriented Sensitivity Analysis (QOSA). QOSA indices are relevant in order to quantify uncertainty on quantiles, for example in insurance operational risk contexts. We shall present several view points on conditional quantile estimation: quantile regression and improvements, Kernel based estimation, random forest estimation. We shall focus on applications to QOSA.
Estimation of conditional quantiles is requiered for many purposes, in particular when the conditional mean is not suffisiant to describe the impact of covariates on the dependent variable. For example, one may estimate the quantile of one financial index (e.g. WisdomTree Japan Hedged Equity Fund) knowing financial indeces from other countries. It is also requiered to estimated conditional quantiles in Quantile Oriented Sensitivity Analysis ...

62-07 ; 62G20

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Estimation of conditional quantiles is requiered for many purposes, in particular when the conditional mean is not suffisiant to describe the impact of covariates on the dependent variable. For example, one may estimate the quantile of one financial index (e.g. WisdomTree Japan Hedged Equity Fund) knowing financial indeces from other countries. It is also requiered to estimated conditional quantiles in Quantile Oriented Sensitivity Analysis (QOSA). QOSA indices are relevant in order to quantify uncertainty on quantiles, for example in insurance operational risk contexts. We shall present several view points on conditional quantile estimation: quantile regression and improvements, Kernel based estimation, random forest estimation. We shall focus on applications to QOSA.
Estimation of conditional quantiles is requiered for many purposes, in particular when the conditional mean is not suffisiant to describe the impact of covariates on the dependent variable. For example, one may estimate the quantile of one financial index (e.g. WisdomTree Japan Hedged Equity Fund) knowing financial indeces from other countries. It is also requiered to estimated conditional quantiles in Quantile Oriented Sensitivity Analysis ...

62-07 ; 62G20

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Virtualconference  A splitting theorem
Druel, Stéphane (Auteur de la Conférence) | CIRM (Editeur )

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The decomposition theorem gives some insight on the structure of compact Kähler manifolds with trivial first Chern class. In the first part of the talk I will try to summarize the history of the problem, from the Calabi conjecture to its proof by Yau; in the second part I will explain why the result is an easy consequence of Yau's theorem.

14J32 ; 53C26

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​The purpose of the discussion session is to discuss how the proof of the decomposition theorem came to be

14-06

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Presentation of open problems on the subject, intertwined with comments by the speakers of the workshop.

14-06

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The notion of a Poisson manifold originated in mathematical physics, where it is used to describe the equations of motion of classical mechanical systems, but it is nowadays connected with many different parts of mathematics. A key feature of any Poisson manifold is that it carries a canonical foliation by even-dimensional submanifolds, called its symplectic leaves. They correspond physically to regions in phase space where the motion of a particle is trapped.

I will give an introduction to Poisson manifolds in the context of complex analytic/algebraic geometry, with a particular focus on the geometry of the associated foliation. Starting from basic definitions and constructions, we will see many examples, leading to some discussion of recent progress towards the classification of Poisson brackets on Fano manifolds of small dimension, such as projective space.
The notion of a Poisson manifold originated in mathematical physics, where it is used to describe the equations of motion of classical mechanical systems, but it is nowadays connected with many different parts of mathematics. A key feature of any Poisson manifold is that it carries a canonical foliation by even-dimensional submanifolds, called its symplectic leaves. They correspond physically to regions in phase space where the motion of a ...

53D17 ; 37F75 ; 14J10

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The notion of a Poisson manifold originated in mathematical physics, where it is used to describe the equations of motion of classical mechanical systems, but it is nowadays connected with many different parts of mathematics. A key feature of any Poisson manifold is that it carries a canonical foliation by even-dimensional submanifolds, called its symplectic leaves. They correspond physically to regions in phase space where the motion of a particle is trapped.

I will give an introduction to Poisson manifolds in the context of complex analytic/algebraic geometry, with a particular focus on the geometry of the associated foliation. Starting from basic definitions and constructions, we will see many examples, leading to some discussion of recent progress towards the classification of Poisson brackets on Fano manifolds of small dimension, such as projective space.
The notion of a Poisson manifold originated in mathematical physics, where it is used to describe the equations of motion of classical mechanical systems, but it is nowadays connected with many different parts of mathematics. A key feature of any Poisson manifold is that it carries a canonical foliation by even-dimensional submanifolds, called its symplectic leaves. They correspond physically to regions in phase space where the motion of a ...

37F75 ; 53D17 ; 14J10

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The notion of a Poisson manifold originated in mathematical physics, where it is used to describe the equations of motion of classical mechanical systems, but it is nowadays connected with many different parts of mathematics. A key feature of any Poisson manifold is that it carries a canonical foliation by even-dimensional submanifolds, called its symplectic leaves. They correspond physically to regions in phase space where the motion of a particle is trapped.

I will give an introduction to Poisson manifolds in the context of complex analytic/algebraic geometry, with a particular focus on the geometry of the associated foliation. Starting from basic definitions and constructions, we will see many examples, leading to some discussion of recent progress towards the classification of Poisson brackets on Fano manifolds of small dimension, such as projective space.
The notion of a Poisson manifold originated in mathematical physics, where it is used to describe the equations of motion of classical mechanical systems, but it is nowadays connected with many different parts of mathematics. A key feature of any Poisson manifold is that it carries a canonical foliation by even-dimensional submanifolds, called its symplectic leaves. They correspond physically to regions in phase space where the motion of a ...

37F75 ; 53D17 ; 14J10

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In the last few decades, much progress has been made in birational algebraic geometry. The general viewpoint is that complex projective manifolds should be classified according to the behavior of their canonical class. As a result of the minimal model program (MMP), every complex projective manifold can be built up from 3 classes of (possibly singular) projective varieties, namely, varieties $X$ for which $K_X$ satisfies $K_X<0$, $K_X\equiv 0$ or $K_X>0$. Projective manifolds $X$ whose anti-canonical class $-K_X$ is ample are called Fano manifolds.

Techniques from the MMP have been successfully applied to the study of global properties of holomorphic foliations. This led, for instance, to Brunella's birational classification of foliations on surfaces, in which the canonical class of the foliation plays a key role. In recent years, much progress has been made in higher dimensions. In particular, there is a well developed theory of Fano foliations, i.e., holomorphic foliations $F$ on complex projective varieties with ample anti-canonical class $-K_F$.

This mini-course is devoted to reviewing some aspects of the theory of Fano Foliations, with a special emphasis on Fano foliations of large index. We start by proving a fundamental algebraicity property of Fano foliations, as an application of Bost's criterion of algebraicity for formal schemes. We then introduce and explore the concept of log leaves. These tools are then put together to address the problem of classifying Fano foliations of large index.
In the last few decades, much progress has been made in birational algebraic geometry. The general viewpoint is that complex projective manifolds should be classified according to the behavior of their canonical class. As a result of the minimal model program (MMP), every complex projective manifold can be built up from 3 classes of (possibly singular) projective varieties, namely, varieties $X$ for which $K_X$ satisfies $K_X0$. Projective manifo...

37F75

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In the last few decades, much progress has been made in birational algebraic geometry. The general viewpoint is that complex projective manifolds should be classified according to the behavior of their canonical class. As a result of the minimal model program (MMP), every complex projective manifold can be built up from 3 classes of (possibly singular) projective varieties, namely, varieties $X$ for which $K_X$ satisfies $K_X<0$, $K_X\equiv 0$ or $K_X>0$. Projective manifolds $X$ whose anti-canonical class $-K_X$ is ample are called Fano manifolds.

Techniques from the MMP have been successfully applied to the study of global properties of holomorphic foliations. This led, for instance, to Brunella's birational classification of foliations on surfaces, in which the canonical class of the foliation plays a key role. In recent years, much progress has been made in higher dimensions. In particular, there is a well developed theory of Fano foliations, i.e., holomorphic foliations $F$ on complex projective varieties with ample anti-canonical class $-K_F$.

This mini-course is devoted to reviewing some aspects of the theory of Fano Foliations, with a special emphasis on Fano foliations of large index. We start by proving a fundamental algebraicity property of Fano foliations, as an application of Bost's criterion of algebraicity for formal schemes. We then introduce and explore the concept of log leaves. These tools are then put together to address the problem of classifying Fano foliations of large index.
In the last few decades, much progress has been made in birational algebraic geometry. The general viewpoint is that complex projective manifolds should be classified according to the behavior of their canonical class. As a result of the minimal model program (MMP), every complex projective manifold can be built up from 3 classes of (possibly singular) projective varieties, namely, varieties $X$ for which $K_X$ satisfies $K_X0$. Projective manifo...

37F75

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