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Post-edited  Self-interacting walks and uniform spanning forests
Peres, Yuval (Auteur de la Conférence) | CIRM (Editeur )

In the first half of the talk, I will survey results and open problems on transience of self-interacting martingales. In particular, I will describe joint works with S. Popov, P. Sousi, R. Eldan and F. Nazarov on the tradeoff between the ambient dimension and the number of different step distributions needed to obtain a recurrent process. In the second, unrelated, half of the talk, I will present joint work with Tom Hutchcroft, showing that the component structure of the uniform spanning forest in $\mathbb{Z}^d$ changes every dimension for $d > 8$. This sharpens an earlier result of Benjamini, Kesten, Schramm and the speaker (Annals Math 2004), where we established a phase transition every four dimensions. The proofs are based on a the connection to loop-erased random walks. In the first half of the talk, I will survey results and open problems on transience of self-interacting martingales. In particular, I will describe joint works with S. Popov, P. Sousi, R. Eldan and F. Nazarov on the tradeoff between the ambient dimension and the number of different step distributions needed to obtain a recurrent process. In the second, unrelated, half of the talk, I will present joint work with Tom Hutchcroft, showing that the ...

05C05 ; 05C80 ; 60G50 ; 60J10 ; 60K35 ; 82B43

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ques, de ses recherches, de la richesse mathématique marseillaise, de sa collaboration avec Artur Avila (Médaille Fields 2014), etc. Artur Avila que nous avons pu contacter avant l'interview de Pascal Hubert, et qui nous a demandé de lui parler de Jean-Christophe Yoccoz... Pascal Hubert est mathématicien, professeur au sein d'Aix-Marseille Université et directeur de la FRUMAM.
Il parle ici de son grand-père, qui lui a donné le goût des mathématiques, de ses recherches, de la richesse mathématique marseillaise, de sa collaboration avec Artur Avila (Médaille Fields 2014), etc. Artur Avila que nous avons pu contacter avant l'interview de Pascal Hubert, et qui nous a demandé de lui parler de Jean-Christophe Yoccoz...

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Post-edited  Interview at CIRM: Mark Pollicott
Pollicott, Mark (Personne interviewée) | CIRM (Editeur )

Mark Pollicott (born 24 September 1959) is a British mathematician known for his contributions to ergodic theory and dynamical systems. He has a particular interest in applications to other areas of mathematics, including geometry, number theory and analysis.

Pollicott attended High Pavement College in Nottingham, where his teachers included the Booker prize winning author Stanley Middleton. He gained a BSc in Mathematics and Physics in 1981 and a PhD in Mathematics in 1984 both at the University of Warwick. His PhD supervisor was Bill Parry and his thesis title The Ruelle Operator, Zeta Functions and the Asymptotic Distribution of Closed Orbits.

He held permanent positions at the University of Edinburgh, University of Porto, and University of Warwick before appointment to the Fielden Chair of Pure Mathematics in Manchester (1996-2004). He then returned to a professorship at Warwick in 2005. In addition, he has held numerous visiting positions including ones at the IHES in Paris, the Institute for Advanced Study in Princeton, MSRI in University of California, Berkeley, Caltech and Grenoble. He has been recipient of a Royal Society University Research Fellowship, two Leverhulme Trust Senior Research Fellowships and an E.U. Marie Curie Chair.
Mark Pollicott (born 24 September 1959) is a British mathematician known for his contributions to ergodic theory and dynamical systems. He has a particular interest in applications to other areas of mathematics, including geometry, number theory and analysis.

Pollicott attended High Pavement College in Nottingham, where his teachers included the Booker prize winning author Stanley Middleton. He gained a BSc in Mathematics and Physics in 1981 ...

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Post-edited  The Onsager Theorem
De Lellis, Camillo (Auteur de la Conférence) | CIRM (Editeur )

In the fifties John Nash astonished the geometers with his celebrated isometric embedding theorems. A folkloristic explanation of his first theorem is that you should be able to put any piece of paper in your pocket without crumpling or folding it, no matter how large it is.
Ten years ago László Székelyhidi and I discovered unexpected similarities with the behavior of some classical equations in fluid dynamics. Our remark sparked a series of discoveries and works which have gone in several directions. Among them the most notable is the recent proof of Phil Isett of a long-standing conjecture of Lars Onsager in the theory of turbulent flows. In a joint work with László, Tristan Buckmaster and Vlad Vicol we improve Isett's theorem to show the existence of dissipative solutions of the incompressible Euler equations below the Onsager's threshold.
In the fifties John Nash astonished the geometers with his celebrated isometric embedding theorems. A folkloristic explanation of his first theorem is that you should be able to put any piece of paper in your pocket without crumpling or folding it, no matter how large it is.
Ten years ago László Székelyhidi and I discovered unexpected similarities with the behavior of some classical equations in fluid dynamics. Our remark sparked a series of ...

35Q31 ; 35D30 ; 76B03

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Post-edited  Detection theory and novelty filters
Morel, Jean-Michel (Auteur de la Conférence) | CIRM (Editeur )

In this presentation based on on-line demonstrations of algorithms and on the examination of several practical examples, I will reflect on the problem of modeling a detection task in images. I will place myself in the (very frequent) case where the detection task can not be formulated in a Bayesian framework or, rather equivalently that can not be solved by simultaneous learning of the model of the object and that of the background. (In the case where there are plenty of examples of the background and of the object to be detected, the neural networks provide a practical answer, but without explanatory power). Nevertheless for the detection without "learning", I will show that we can not avoid building a background model, or possibly learn it. But this will not require many examples.

Joint works with Axel Davy, Tristan Dagobert, Agnes Desolneux, Thibaud Ehret.
In this presentation based on on-line demonstrations of algorithms and on the examination of several practical examples, I will reflect on the problem of modeling a detection task in images. I will place myself in the (very frequent) case where the detection task can not be formulated in a Bayesian framework or, rather equivalently that can not be solved by simultaneous learning of the model of the object and that of the background. (In the case ...

65D18 ; 68U10 ; 68T05

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Post-edited  Large gaps between primes in subsets
Maynard, James (Auteur de la Conférence) | CIRM (Editeur )

All previous methods of showing the existence of large gaps between primes have relied on the fact that smooth numbers are unusually sparse. This feature of the argument does not seem to generalise to showing large gaps between primes in subsets, such as values of a polynomial. We will talk about recent work which allows us to show large gaps between primes without relying on smooth number estimates. This then generalizes naturally to show long strings of consecutive composite values of a polynomial. This is joint work with Ford, Konyagin, Pomerance and Tao. All previous methods of showing the existence of large gaps between primes have relied on the fact that smooth numbers are unusually sparse. This feature of the argument does not seem to generalise to showing large gaps between primes in subsets, such as values of a polynomial. We will talk about recent work which allows us to show large gaps between primes without relying on smooth number estimates. This then generalizes naturally to show long ...

11N05 ; 11N35 ; 11N36

und-color:#088A4B"> Post-edited  Le problème Graph Motif - Partie 1
Fertin, Guillaume (Auteur de la Conférence) | CIRM (Editeur )

Le problème Graph Motif est défini comme suit : étant donné un graphe sommet colorié G=(V,E) et un multi-ensemble M de couleurs, déterminer s'il existe une occurrence de M dans G, c'est-à-dire un sous ensemble V' de V tel que
(1) le multi-ensemble des couleurs de V' correspond à M,
(2) le sous-graphe G' induit par V' est connexe.
Ce problème a été introduit, il y a un peu plus de 10 ans, dans le but de rechercher des motifs fonctionnels dans des réseaux biologiques, comme par exemple des réseaux d'interaction de protéines ou des réseaux métaboliques. Graph Motif a fait depuis l'objet d'une attention particulière qui se traduit par un nombre relativement élevé de publications, essentiellement orientées autour de sa complexité algorithmique.
Je présenterai un certain nombre de résultats algorithmiques concernant le problème Graph Motif, en particulier des résultats de FPT (Fixed-Parameter Tractability), ainsi que des bornes inférieures de complexité algorithmique.
Ceci m'amènera à détailler diverses techniques de preuves dont certaines sont plutôt originales, et qui seront je l'espère d'intérêt pour le public.
Le problème Graph Motif est défini comme suit : étant donné un graphe sommet colorié G=(V,E) et un multi-ensemble M de couleurs, déterminer s'il existe une occurrence de M dans G, c'est-à-dire un sous ensemble V' de V tel que
(1) le multi-ensemble des couleurs de V' correspond à M,
(2) le sous-graphe G' induit par V' est connexe.
Ce problème a été introduit, il y a un peu plus de 10 ans, dans le but de rechercher des motifs fonctionnels dans des ...

05C15 ; 05C85 ; 05C90 ; 68Q17 ; 68Q25 ; 68R10 ; 92C42 ; 92D20