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# Multi angle

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Multi angle A new spectral theory for Schur polynomials and applications

Auteurs : Moll, Alexander (Auteur de la Conférence)
CIRM (Editeur )

Résumé : After Fourier series, the quantum Hopf-Burgers equation $v_t +vv_x = 0$ with periodic boundary conditions is equivalent to a system of coupled quantum harmonic oscillators, which may be prepared in Glauber's coherent states as initial conditions. Sending the displacement of each oscillator to infinity at the same rate, we (1) confirm and (2) determine corrections to the quantum-classical correspondence principle. After diagonalizing the Hamiltonian with Schur polynomials, this is equivalent to proving (1) the concentration of profiles of Young diagrams around a limit shape and (2) their global Gaussian fluctuations for Schur measures with symbol $v : T \to R$ on the unit circle $T$. We identify the emergent objects with the push-forward along $v$ of (1) the uniform measure on $T$ and (2) $H^{1/2}$ noise on $T$. Our proofs exploit the integrability of the model as described by Nazarov-Sklyanin (2013). As time permits, we discuss structural connections to the theory of the topological recursion.

Codes MSC :
05E10 - Combinatorial aspects of representation theory
37K10 - Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.)
20G43 - Schur and $q$-Schur algebras

 Informations sur la Vidéo Réalisateur : Hennenfent, Guillaume Langue : Anglais Date de publication : 17/01/17 Date de captation : 10/01/17 Collection : Research schools Format : MP4 Durée : 00:51:29 Domaine : Combinatorics ; Dynamical Systems & ODE Audience : Chercheurs ; Doctorants , Post - Doctorants Download : http://videos.cirm-math.fr/2017-01-10_Moll.mp4 Informations sur la rencontre Nom du congrès : Winter pre-school on combinatorics and interactions / Ecole d'hiver combinatoire et interactionsOrganisteurs Congrès : Bouttier, Jérémie ; Chapuy, Guillaume ; Duchi, EnricaDates : 09/01/17 - 13/01/17 Année de la rencontre : 2017 URL Congrès : http://conferences.cirm-math.fr/1554.htmlCitation DataDOI : 10.24350/CIRM.V.19103003Cite this video as: Moll, Alexander (2017). A new spectral theory for Schur polynomials and applications. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19103003URI : http://dx.doi.org/10.24350/CIRM.V.19103003

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