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Videothèque  | enregistrements trouvés : 12

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For negatively curved Riemannian manifolds, Margulis gave an asymptotic formula for the number of closed geodesics with length below a given threshold. I will describe joint work with Gerhard Knieper and Khadim War in which we obtain the corresponding result for surfaces without conjugate points by first proving uniqueness of the measure of maximal entropy and then following the approach of recent work by Russell Ricks, who established the asymptotic estimates in the setting of CAT(0) geodesic flows.
For negatively curved Riemannian manifolds, Margulis gave an asymptotic formula for the number of closed geodesics with length below a given threshold. I will describe joint work with Gerhard Knieper and Khadim War in which we obtain the corresponding result for surfaces without conjugate points by first proving uniqueness of the measure of maximal entropy and then following the approach of recent work by Russell Ricks, who established the ...

53D25 ; 37D40

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Joint work with Guillarmou and Lefeuvre.

37D40

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The talk will review recent work on intermediate dimensions which interpolate between Hausdorff and box dimensions. We relate these dimensions to capacities which leading to ‘Marstrand-type’ theorems on the intermediate dimensions of projections of a set in $\mathbb{R}^{n}$ onto almost all m-dimensional subspaces. This is collaborative work with various combinations of Stuart Burrell, Jonathan Fraser, Tom Kempton and Pablo Shmerkin.

28A80 ; 28A78 ; 28A75

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Multifractal properties of data coming from many scientific fields (especially in turbulence) are now rigorously established. Unfortunately, the parameters measured on these data do not correspond to those mathematically obtained for the typical (or almost sure) functions in the standard functional spaces: Hölder, Sobolev, Besov…
In this talk, we introduce very natural Besov spaces in which typical functions possess very rich scaling properties, mimicking those observed on data for instance. We obtain various characterizations of these function spaces, in terms of oscillations or wavelet coefficients.
Combining this with the construction of almost-doubling measures with prescribed scaling properties, we are able to bring a solution to the so-called Frisch-Parisi conjecture. This is a joint work with Julien Barral (Université Paris-Nord).
Multifractal properties of data coming from many scientific fields (especially in turbulence) are now rigorously established. Unfortunately, the parameters measured on these data do not correspond to those mathematically obtained for the typical (or almost sure) functions in the standard functional spaces: Hölder, Sobolev, Besov…
In this talk, we introduce very natural Besov spaces in which typical functions possess very rich scaling properties, ...

37F35

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Multi angle  Random perturbation of low-rank matrices
Wang, Ke (Auteur de la Conférence) | CIRM (Editeur )

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Multi angle  Problems with continuous quantum walks
Godsil, Chris (Auteur de la Conférence) | CIRM (Editeur )

Continuous quantum walks are of great interest in quantum computing and, over the last decade, my group has been studying this topic intensively. As graph theorists, one of our main goals has been to get a better understanding of the relation between the properties of a walk and the properties of the underlying graph. We have had both successes and failures. The failures lead to a number of interesting open questions, which I will present in my talk.
Continuous quantum walks are of great interest in quantum computing and, over the last decade, my group has been studying this topic intensively. As graph theorists, one of our main goals has been to get a better understanding of the relation between the properties of a walk and the properties of the underlying graph. We have had both successes and failures. The failures lead to a number of interesting open questions, which I will present in my ...

05C50 ; 81Q35

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Multi angle  Time-multiplexed quantum walks
Silberhorn, Christine (Auteur de la Conférence) | CIRM (Editeur )

Photonic quantum systems, which comprise multiple optical modes, have become an established platform for the experimental implementation of quantum walks. However, the implementation of large systems with many modes, this means for many step operations, a high and dynamic control of many different coin operations and variable graph structures typically poses a considerable challenge.
Time-multiplexed quantum walks are a versatile tool for the implementation of a highly flexible simulation platform with dynamic control of the different graph structures and propagation properties. Our time-multiplexing techniques is based on a loop geometry ensures a extremely high homogeneity of the quantum walk system, which results in highly reliable walk statistics. By introducing optical modulators we can control the dynamics of the photonic walks as well as input and output couplings of the states at different stages during the evolution of the walk.
Here we present our recent results on our time-multiplexed quantum walk experiments.
Photonic quantum systems, which comprise multiple optical modes, have become an established platform for the experimental implementation of quantum walks. However, the implementation of large systems with many modes, this means for many step operations, a high and dynamic control of many different coin operations and variable graph structures typically poses a considerable challenge.
Time-multiplexed quantum walks are a versatile tool for the ...

82C10

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The coined quantum walk is a discretization of the Dirac equation of relativistic quantum mechanics, and it is a useful model for developing quantum algorithms. For example, many quantum spatial search algorithms are based on coined quantum walks. In this talk, we explore a lazy version of the coined quantum walk, called a lackadaisical quantum walk, which uses a weighted self-loop at each vertex so that the walker has some amplitude of staying put. We show that lackadaisical quantum walks can solve the spatial search problem more quickly than a regular, coined quantum walk for avariety of graphs, suggesting that it is a useful tool for improving quantum algorithms.
The coined quantum walk is a discretization of the Dirac equation of relativistic quantum mechanics, and it is a useful model for developing quantum algorithms. For example, many quantum spatial search algorithms are based on coined quantum walks. In this talk, we explore a lazy version of the coined quantum walk, called a lackadaisical quantum walk, which uses a weighted self-loop at each vertex so that the walker has some amplitude of staying ...

81Q35

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