Upcoming talks

• Date: 4/16/99
  • Speaker: Henrik Shahgholian, Royal Institute of Technology, Stockholm
  • Title: On the porosity of free boundaries in degenerate variational
    inequalities
  • Abstract:
    In this talk we consider a certain degenerate variational problem
    with zero constraint. The exact growth of the solution near the free
    boundary will be established. As a consequence of this we show that the
    free boundary is porous and therefore its Hausdorff dimension is less than
    $N$ and hence it is of Lebesgue measure zero.

    Keywords: Obstacle problem, nonhomogeneous $p$-Laplace equation, free boundary,
    porosity.

• Date: 4/22/99, Mathematics Colloquium, SH 6635, 3:30-4:30pm
  • Speaker: Hans Wenzl, UCSD
  • Title: Braids, Categories and Invariants
  • Abstract: Classically, symmetric groups were used to
    describe the decomposition of tensor products of representations
    of the general linear group. A similar and more general interplay
    exists between braid groups and quantum groups.
    This way one obtains an elementary construction of fusion categories
    (for classical Lie types), which in turn can be used to construct
    invariants of links and 3-manifolds, and subfactors.
• Date: 4/23/99
  • Speaker: Hans Wenzl, UCSD
  • Title: Tensor categories for exceptional Lie groups
  • Abstract: While tensor categories related to classical Lie groups
    have been well studied, the ones for exceptional Lie groups still are
    quite mysterious. Inspired by Vogel’s work on finite type link invariants,
    Deligne proposed to study the 5 exceptional Lie groups simultaneously
    in an `exceptional series’. We describe his evidence for such a series,
    and how one can obtain additional information from braid groups by extending
    this approach to the quantum setting.
• Date: 4/30/99
  • Speaker: Dan Voiculescu, UC Berkeley
  • Title: Topics in free entropy : liberation and mutual free
    information
• Date: 5/3/99, Advancement to Candidacy, 1:00-3:00 pm, SH 4607 !!
  • Speaker: Anne Louise Svendsen
  • Title: Analytical properties of the standard invariant for subfactors
• Date: 5/7/99
  • Speaker: Joerg Eschmeier, Universitaet Saarbruecken
  • Title: Invariant subspaces for commuting contractions
  • Abstract:
    A classical result of Brown, Chevreau
    and Pearcy shows that each contraction on a Hilbert
    space with dominating spectrum in the open unit
    disc possesses a non-trivial closed invariant
    subspace. As an application of the Scott Brown
    technique we prove corresponding invariant-subspace
    results for commuting systems of contractions and
    for spherical contractions. We indicate that
    subnormal n-tuples with rich spectrum in the
    unit ball or unit polydisc are reflexive.
• Date: 5/14/99
  • no meeting
• Date: 5/21/99
  • Speaker: Sorin Popa, UCLA
  • Title: Universal constructions of subfactors
• Date: 5/28/99
  • Speaker: Peyman Milanfar, SRI – Stanford
  • Title: Connections Between Inverse Problems, Moments, and Array Signal
    Processing
  • Abstract:
    Much of what we learn about the world is measured indirectly. Inverse
    problems are termed as such because they are concerned with solving
    for the “cause” of a measured physical “effect”. Inverse problems
    arise in many diverse areas of science and engineering, including
    geophysical exploration, astronomy, medicine, and computational vision.
    In this talk, I will explore a class of inverse problems and show
    how the respective measurements can be distilled into moments of the
    underlying quantities we seek to reconstruct. Hence, these measurements
    can directly yield geometric information about the underlying
    object(s) of interest. In turn, I will discuss some deep connections
    between the problem of inverting a shape or function from its moments
    and two apparently disparate areas: 1) numerical quadrature in the
    plane, and 2) array signal processing.

    As a result of these observations, I will demonstrate, in two
    different contexts — computed tomography and gravimetric inversion —
    how the shape of a region may be reconstructed from X-ray attenuation
    or gravitational field measurements respectively, using stable and
    efficient numerical algorithms akin to those used in array
    signal processing. In this way, both new physical interpretations and
    new algorithms for these inverse problems are derived.

• Date: 6/4/99
  • Speaker: Bruce Reznick, UIUC
  • Title: Cones of polynomials in several variables
  • Abstract:
    We will discuss some closed convex cones of real homogeneous
    polynomials in several variables (e.g. the cone of psd forms, the cone
    of sums of squares, the cone of sums of powers of linear forms), as well as
    what appears to be the “right” inner product to place on them. Topics
    touched on will include Hilbert’s 17th Problem, Moment Problems and
    the still-open question of determining which real polynomials in a
    single variable can be written as a sum of fourth powers of
    polynomials. Partial result: there exist real $(a_k,b_k,c_k)$ so that
    $t^8 + ct^4 + 1 = \sum_k(a_kt^2 + b_kt + c_k)^4$ if and only if $c \ge -14/9$.