Past Seminars- Analysis

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  • Bernard Russo
    Tue Oct 16, 2012
    2:00 pm
    A quantum Banach space (operator space for short) is a linear subspace of Hilbert space operators together with its induced matrix norm structure. It is said to be a quantum operator algebra (operator algebra for short) if it is closed under multiplication. In a joint work with Matt Neal, a necessary and sufficient condition is given for a...
  • Yuan Zhang
    Tue May 29, 2012
    3:00 pm
    In this talk, we study Cauchy-Riemann equation on some smooth convex domains of in nite type in C2. In detail, we show that supnorm estimates hold for those infi nite exponential type domains provided the exponent is less than 1. This is a joint work with John Erik Fornaess and Lina Lee.
  • Bernard Russo
    Tue Apr 17, 2012
    3:00 pm
    I will present elementary (classical) proof(s) that every derivation of a finite dimensional semisimple algebra (associative, Lie, or Jordan) is inner, and state what is known in infinite dimensions for operator algebras. Then I will do the same for the corresponding triple systems. The purpose is to set the stage for the study of continuous...
  • Professor Sagun Chanillo
    Thu Apr 12, 2012
    3:00 pm
    We consider the global embedding problem for compact, three dimensional CR manifolds. Sufficient conditions for embeddability are obtained from assumptions on the CR Yamabe invariant and the non-negativity of a certain conformally invariant fourth order operator called the CR Paneitz operator. The conditions are shown to be necessary for small...
  • Baoping Liu
    Tue Mar 13, 2012
    3:00 pm
    In this talk, I will review the regularity problem for Korteweg-de Vries (KdV) equation on the line, and give a brief summary of the sharp well-posedness and ill-posedness results. Then I will discuss a possible way to get a-priori bounds and weak solution below the critical threshold H^{-3/4}.
  • Alexei Ilyin
    Tue Mar 6, 2012
    3:00 pm
    We discuss some resent results for two type of spectral inequalities in connection with the Navier-Stokes equations. Namely, the Berezin-Li-Yau inequalities for the eigenvalues of elliptic equations and systems ( including the Stokes system) with constant coefficients and the Lieb-Thirring inequalities for the negative spectrum of the Schrodinger...
  • Dr. Son Duong
    Tue Feb 21, 2012
    3:00 pm
    We investigate the transversality of holomorphic mappings between CR submanifolds of complex spaces. In equidimension case, we show that a holomorphic mapping sending one generic submanifold into another of the same dimension is CR transversal to the target submanifold, provided that the source manifold is of finite type and the map is of generic...