00:00:00 / 00:00:00

A new spectral theory for Schur polynomials and applications

By Alexander Moll

Appears in collections : Winter pre-school on combinatorics and interactions / Ecole d'hiver combinatoire et interactions, Ecoles de recherche

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.

Information about the video

Citation data

  • DOI 10.24350/CIRM.V.19103003
  • Cite this video Moll, Alexander (10/01/2017). A new spectral theory for Schur polynomials and applications. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19103003
  • URL https://dx.doi.org/10.24350/CIRM.V.19103003

Last related questions on MathOverflow

You have to connect your Carmin.tv account with mathoverflow to add question

Ask a question on MathOverflow




Register

  • Bookmark videos
  • Add videos to see later &
    keep your browsing history
  • Comment with the scientific
    community
  • Get notification updates
    for your favorite subjects
Give feedback