F Nous contacter


0

Videothèque  | enregistrements trouvés : 8

O
     

-A +A

Sélection courante (0) : Tout sélectionner / Tout déselectionner

P Q

Certain quantum spectral problems have the remarkable property that the formal perturbative series for the energy spectrum can be used to generate all other terms in the entire trans-series, in a completely constructive manner. I explain a geometric all-orders WKB approach to these perturbative/non-perturbative relations, which reveals surprising connections to number theory and modular forms.

81T15 ; 81T16 ; 81Q20

Multi angle  Combinatorics of Feynman integrals
Broadhurst, David (Auteur de la Conférence) | CIRM (Editeur )

Very recently, David Roberts and I have discovered wonderful conditions imposed on Feynman integrals by Betti and de Rham homology. In decoding the corresponding matrices, we encounter asymptotic expansions of a refined nature. In making sense of these, we appear to have some refuge in resurgence.

81T18 ; 05Axx

Rooted connected chord diagrams can be used to index certain expansions in quantum field theory. There is also a nice bijection between rooted connected chord diagrams and bridgeless maps. I will discuss each of these things as well as how the second sheds light on the first. (Based on work with Nicolas Marie, Markus Hihn, Julien Courtiel, and Noam Zeilberger.)

81T15 ; 81T18 ; 05C80

The Hopf algebra of Lie group integrators has been introduced by H. Munthe-Kaas and W. Wright as a tool to handle Runge-Kutta numerical methods on homogeneous spaces. It is spanned by planar rooted forests, possibly decorated. We will describe a canonical surjective Hopf algebra morphism onto the shuffle Hopf algebra which deserves to be called planar arborification. The space of primitive elements is a free post-Lie algebra, which in turn will permit us to describe the corresponding co-arborification process.
Joint work with Charles Curry (NTNU Trondheim), Kurusch Ebrahimi-Fard (NTNU) and Hans Z. Munthe-Kaas (Univ. Bergen).
The two triangles appearing at 24'04" and 25'19'' respectively should be understood as a #.
The Hopf algebra of Lie group integrators has been introduced by H. Munthe-Kaas and W. Wright as a tool to handle Runge-Kutta numerical methods on homogeneous spaces. It is spanned by planar rooted forests, possibly decorated. We will describe a canonical surjective Hopf algebra morphism onto the shuffle Hopf algebra which deserves to be called planar arborification. The space of primitive elements is a free post-Lie algebra, which in turn will ...

81T15 ; 16T05 ; 17D25 ; 65L06 ; 05C05

Inspired by a recent result of Dodson-Luhrmann-Mendelson, who proved almost sure scattering for the energy-critical wave equation with radial data in four dimensions, we establish the analogous result for the Schrödinger equation.
This is joint work with R. Killip and J. Murphy.

35Q55 ; 35L05 ; 35R60

It has been observed by physicists (Isaacson, Burnett, Green-Wald) that metric perturbations of a background solution, which are small amplitude but with high frequency, yield at the limit to a non trivial contribution which corresponds to the presence of an energy impulsion tensor in the equation for the background metric. This non trivial contribution is of due to the nonlinearities in Einstein equations, which involve products of derivatives of the metric. It has been conjectured by Burnett that the only tensors which can be obtained this way are massless Vlasov, and it has been proved by Green and Wald that the limit tensor must be traceless and satisfy the dominant energy condition. The known exemples of this phenomena are constructed under symmetry reductions which involve two Killing fields and lead to an energy impulsion tensor which consists in at most two dust fields propagating in null directions. In this talk, I will explain our construction, under a symmetry reduction involving one Killing field, which leads to an energy impulsion tensor consisting in N dust fields propagating in arbitrary null directions. This is a joint work with Jonathan Luk (Stanford). It has been observed by physicists (Isaacson, Burnett, Green-Wald) that metric perturbations of a background solution, which are small amplitude but with high frequency, yield at the limit to a non trivial contribution which corresponds to the presence of an energy impulsion tensor in the equation for the background metric. This non trivial contribution is of due to the nonlinearities in Einstein equations, which involve products of derivatives ...

35Q75 ; 53C80 ; 83C05

The talk will discuss a recent result showing that certain type II blow up solutions constructed by Krieger-Schlag-Tataru are actually stable under small perturbations along a co-dimension one Lipschitz hypersurface in a suitable topology. This result is qualitatively optimal.
Joint work with Stefano Burzio (EPFL).

35L05 ; 35B40

Multi angle  Geometric heat flows and caloric gauges
Tataru, Daniel (Auteur de la Conférence) | CIRM (Editeur )

Choosing favourable gauges is a crucial step in the study of nonlinear geometric dispersive equations. A very successful tool, that has emerged originally in work of Tao on wave maps, is the use of caloric gauges, defined via the corresponding geometric heat flows. The aim of this talk is to describe two such flows and their associated gauges, namely the harmonic heat flow and the Yang-Mills heat flow.

70S15 ; 35Q53 ; 35Q55

Nuage de mots clefs ici

Z