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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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Z
Conférence) | CIRM (Editeur )

Birch gave an extremely efficient algorithm to compute a certain subspace of classical modular forms using the Hecke action on classes of ternary quadratic forms. We extend this method to compute all forms of non-square level using the spinor norm, and we exhibit an implementation that is very fast in practice. This is joint work with Jeffery Hein and Gonzalo Tornaria.

11E20 ; 11F11 ; 11F37 ; 11F27

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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 ...

37K10 ; 35C07 ; 35C08 ; 35Q53 ; 35Q55 ; 76B15 ; 76Fxx

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Post-edited  Spectral theory and semi-classical analysis for the complex Schrödinger operator
Helffer, Bernard (Auteur de la Conférence) | CIRM (Editeur )

We consider the operator $\mathcal{A}_h = -h^2 \Delta + iV$ in the semi-classical limit $h \to 0$, where $V$ is a smooth real potential with no critical points. We obtain both the left margin of the spectrum, as well as resolvent estimates on the left side of this margin. We extend here previous results obtained for the Dirichlet realization of $\mathcal{A}_h$ by removing significant limitations that were formerly imposed on $V$. In addition, we apply our techniques to the more general Robin boundary condition and to a transmission problem which is of significant interest in physical applications. We consider the operator $\mathcal{A}_h = -h^2 \Delta + iV$ in the semi-classical limit $h \to 0$, where $V$ is a smooth real potential with no critical points. We obtain both the left margin of the spectrum, as well as resolvent estimates on the left side of this margin. We extend here previous results obtained for the Dirichlet realization of $\mathcal{A}_h$ by removing significant limitations that were formerly imposed on $V$. In addition, ...

35J10 ; 35P10 ; 35P15 ; 47A10 ; 81Q12 ; 82D55

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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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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

s $\omega$-categories freely generated by polygraphs and introduce the key notion of polygraphic resolution. Finally, by considering a monoid as a particular $\omega$-category, this polygraphic point of view will lead us to an alternative definition ...

18D05 ; 18G55 ; 18G50 ; 18G10