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Multi angle  Dynamics on homogeneous spaces and Diophantine approximation
Ghosh, Anish (Auteur de la Conférence) | CIRM (Editeur )

I will discuss approaches to several problems concerning values of linear and quadratic forms using the ergodic theory of group actions on the space of unimodular lattices, and more generally, on homogeneous spaces of semisimple Lie groups.

37A17 ; 11K60 ; 22F30

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Multi angle  Dynamics on quotients of SL(2,C) by discrete subgroups - Lecture 2
Schapira, Barbara (Auteur de la Conférence) | CIRM (Editeur )

We will discuss old and recent results on topological and measurable dynamics of diagonal and unipotent flows on frame bundles and unit tangent bundles over hyperbolic manifolds. The first lectures will be a good introduction to the subject for young researchers.

37D40 ; 37A17 ; 37A25

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Multi angle  Shrinking targets on homogeneous spaces and improving Dirichlet's Theorem
Kleinbock, Dmitry (Auteur de la Conférence) | CIRM (Editeur )

Optimal results on the improvements to Dirichlet's Theorem are obtained in the one-dimensional case. For simultaneous approximation the problem is open. I will describe reduction of the problem to dynamics both in one-dimensional case (via continued fractions) and for higher dimensions (via diagonal flows on the space of lattices). If time allows I'll mention an inhomogeneous version which is easier than the homogeneous one. Joint work with Nick Wadleigh. Optimal results on the improvements to Dirichlet's Theorem are obtained in the one-dimensional case. For simultaneous approximation the problem is open. I will describe reduction of the problem to dynamics both in one-dimensional case (via continued fractions) and for higher dimensions (via diagonal flows on the space of lattices). If time allows I'll mention an inhomogeneous version which is easier than the homogeneous one. Joint work with Nick ...

22F30 ; 11J04 ; 11J70 ; 37A17

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Multi angle  Counting and equidistribution of integral representations by quadratic norm forms in positive characteristic?
Paulin, Frédéric (Auteur de la Conférence) | CIRM (Editeur )

In this talk, we will prove the projective equidistribution of integral representations by quadratic norm forms in positive characteristic, with error terms, and deduce asymptotic counting results of these representations. We use the ergodic theory of lattice actions on Bruhat-Tits trees, and in particular the exponential decay of correlation of the geodesic flow on trees for Hölder variables coming from symbolic dynamics techniques.

20E08 ; 11J61 ; 37A25 ; 20G25 ; 37D40

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Multi angle  Mutually enriching connections between ergodic theory and combinatorics - part 4
Bergelson, Vitaly (Auteur de la Conférence) | CIRM (Editeur )

* The early results of Ramsey theory :

Hilbert's irreducibility theorem, Dickson-Schur work on Fermat's equation over finite fields, van der Waerden's theorem, Ramsey's theoremand its rediscovery by Erdos and Szekeres.


* Three main principles of Ramsey theory :

First principle: Complete disorder is impossible. Second principle: Behind every 'Partition' result there is a notion of largeness which is responsible for a 'Density' enhancement of this result. Third principle: The sought-after configurations which are always to be found in large sets are abundant.


* Furstenberg's Dynamical approach :

Partition Ramsey theory and topological dynamics Dynamical versions of van der Waerden's theorem, Hindman's theorem and Graham-Rothschild-Spencer's geometric Ramsey.
Density Ramsey theory and Furstenberg's correspondence principle Furstenberg's correspondence principle. Ergodic Szemeredi's theorem. Polynomial Szemeredi theorem. Density version of the Hales-Jewett theorem.


* Stone-Cech compactifications and Hindman's theorem :

Topological algebra in Stone-Cech compactifications. Proof of Hind-man's theorem via Poincare recurrence theorem for ultrafilters.


* IP sets and ergodic Ramsey theory :

Applications of IP sets and idempotent ultrafilters to ergodic-theoretical multiple recurrence and to density Ramsey theory. IP-polynomial Szemeredi theorem.


* Open problems and conjectures


If time permits: * The nilpotent connection, * Ergodic Ramsey theory and amenable groups
* The early results of Ramsey theory :

Hilbert's irreducibility theorem, Dickson-Schur work on Fermat's equation over finite fields, van der Waerden's theorem, Ramsey's theoremand its rediscovery by Erdos and Szekeres.


* Three main principles of Ramsey theory :

First principle: Complete disorder is impossible. Second principle: Behind every 'Partition' result there is a notion of largeness which is responsible for a 'Density' enhancement of ...

05D10 ; 37Axx ; 12D10 ; 11D41 ; 54D80 ; 37B20

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Multi angle  Mutually enriching connections between ergodic theory and combinatorics - part 5
Bergelson, Vitaly (Auteur de la Conférence) | CIRM (Editeur )

* The early results of Ramsey theory :

Hilbert's irreducibility theorem, Dickson-Schur work on Fermat's equation over finite fields, van der Waerden's theorem, Ramsey's theoremand its rediscovery by Erdos and Szekeres.


* Three main principles of Ramsey theory :

First principle: Complete disorder is impossible. Second principle: Behind every 'Partition' result there is a notion of largeness which is responsible for a 'Density' enhancement of this result. Third principle: The sought-after configurations which are always to be found in large sets are abundant.


* Furstenberg's Dynamical approach :

Partition Ramsey theory and topological dynamics Dynamical versions of van der Waerden's theorem, Hindman's theorem and Graham-Rothschild-Spencer's geometric Ramsey.
Density Ramsey theory and Furstenberg's correspondence principle Furstenberg's correspondence principle. Ergodic Szemeredi's theorem. Polynomial Szemeredi theorem. Density version of the Hales-Jewett theorem.


* Stone-Cech compactifications and Hindman's theorem :

Topological algebra in Stone-Cech compactifications. Proof of Hind-man's theorem via Poincare recurrence theorem for ultrafilters.


* IP sets and ergodic Ramsey theory :

Applications of IP sets and idempotent ultrafilters to ergodic-theoretical multiple recurrence and to density Ramsey theory. IP-polynomial Szemeredi theorem.


* Open problems and conjectures


If time permits: * The nilpotent connection, * Ergodic Ramsey theory and amenable groups
* The early results of Ramsey theory :

Hilbert's irreducibility theorem, Dickson-Schur work on Fermat's equation over finite fields, van der Waerden's theorem, Ramsey's theoremand its rediscovery by Erdos and Szekeres.


* Three main principles of Ramsey theory :

First principle: Complete disorder is impossible. Second principle: Behind every 'Partition' result there is a notion of largeness which is responsible for a 'Density' enhancement of ...

05D10 ; 37Axx ; 12D10 ; 11D41 ; 54D80 ; 37B20

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Multi angle  Mutually enriching connections between ergodic theory and combinatorics - part 6
Bergelson, Vitaly (Auteur de la Conférence) | CIRM (Editeur )

* The early results of Ramsey theory :

Hilbert's irreducibility theorem, Dickson-Schur work on Fermat's equation over finite fields, van der Waerden's theorem, Ramsey's theoremand its rediscovery by Erdos and Szekeres.


* Three main principles of Ramsey theory :

First principle: Complete disorder is impossible. Second principle: Behind every 'Partition' result there is a notion of largeness which is responsible for a 'Density' enhancement of this result. Third principle: The sought-after configurations which are always to be found in large sets are abundant.


* Furstenberg's Dynamical approach :

Partition Ramsey theory and topological dynamics Dynamical versions of van der Waerden's theorem, Hindman's theorem and Graham-Rothschild-Spencer's geometric Ramsey.
Density Ramsey theory and Furstenberg's correspondence principle Furstenberg's correspondence principle. Ergodic Szemeredi's theorem. Polynomial Szemeredi theorem. Density version of the Hales-Jewett theorem.


* Stone-Cech compactifications and Hindman's theorem :

Topological algebra in Stone-Cech compactifications. Proof of Hind-man's theorem via Poincare recurrence theorem for ultrafilters.


* IP sets and ergodic Ramsey theory :

Applications of IP sets and idempotent ultrafilters to ergodic-theoretical multiple recurrence and to density Ramsey theory. IP-polynomial Szemeredi theorem.


* Open problems and conjectures


If time permits: * The nilpotent connection, * Ergodic Ramsey theory and amenable groups
* The early results of Ramsey theory :

Hilbert's irreducibility theorem, Dickson-Schur work on Fermat's equation over finite fields, van der Waerden's theorem, Ramsey's theoremand its rediscovery by Erdos and Szekeres.


* Three main principles of Ramsey theory :

First principle: Complete disorder is impossible. Second principle: Behind every 'Partition' result there is a notion of largeness which is responsible for a 'Density' enhancement of ...

05D10 ; 37Axx ; 12D10 ; 11D41 ; 54D80 ; 37B20

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

Multi angle  Mutually enriching connections between ergodic theory and combinatorics - part 7
Bergelson, Vitaly (Auteur de la Conférence) | CIRM (Editeur )

* The early results of Ramsey theory :

Hilbert's irreducibility theorem, Dickson-Schur work on Fermat's equation over finite fields, van der Waerden's theorem, Ramsey's theoremand its rediscovery by Erdos and Szekeres.


* Three main principles of Ramsey theory :

First principle: Complete disorder is impossible. Second principle: Behind every 'Partition' result there is a notion of largeness which is responsible for a 'Density' enhancement of this result. Third principle: The sought-after configurations which are always to be found in large sets are abundant.


* Furstenberg's Dynamical approach :

Partition Ramsey theory and topological dynamics Dynamical versions of van der Waerden's theorem, Hindman's theorem and Graham-Rothschild-Spencer's geometric Ramsey.
Density Ramsey theory and Furstenberg's correspondence principle Furstenberg's correspondence principle. Ergodic Szemeredi's theorem. Polynomial Szemeredi theorem. Density version of the Hales-Jewett theorem.


* Stone-Cech compactifications and Hindman's theorem :

Topological algebra in Stone-Cech compactifications. Proof of Hind-man's theorem via Poincare recurrence theorem for ultrafilters.


* IP sets and ergodic Ramsey theory :

Applications of IP sets and idempotent ultrafilters to ergodic-theoretical multiple recurrence and to density Ramsey theory. IP-polynomial Szemeredi theorem.


* Open problems and conjectures


If time permits: * The nilpotent connection, * Ergodic Ramsey theory and amenable groups
* The early results of Ramsey theory :

Hilbert's irreducibility theorem, Dickson-Schur work on Fermat's equation over finite fields, van der Waerden's theorem, Ramsey's theoremand its rediscovery by Erdos and Szekeres.


* Three main principles of Ramsey theory :

First principle: Complete disorder is impossible. Second principle: Behind every 'Partition' result there is a notion of largeness which is responsible for a 'Density' enhancement of ...

05D10 ; 37Axx ; 12D10 ; 11D41 ; 54D80 ; 37B20