Past Seminars- Colloquium

Printer-friendly version
  • Ravi Vakil
    Thu Apr 25, 2013
    4:00 pm
    Given some class of "geometric spaces", we can make a ring as follows. (additive structure)  When U is an open subset of such a space X, [X] = [U] + [(X \ U)]; (multiplicative structure)  [X x Y] = [X] [Y]. In the algebraic setting, this ring (the "Grothendieck ring of varieties")...
  • Leonid Parnovsky
    Thu Apr 4, 2013
    4:00 pm
    I will make a survey of recent results on the spectrum of periodic and, to a smaller extent, almost-periodic operators. I will consider two types of results: 1. Bethe-Sommerfeld Conjecture. For a large class of multidimensional periodic operators the numbers of spectral gaps is finite. 2. Asymptotic behaviour of the integrated density of states...
  • Fuquan Fang
    Thu Jan 17, 2013
    4:00 pm
    There is a well known link between (maximal) polar representations and isotropy representations of symmetric spaces provided by Dadok. Moreover, the theory by Tits and Burns-Spatzier provides a link between irreducible symmetric spaces of non-compact type of rank at least three and irreducible topological spherical buildings of rank at least three...
  • Paul Yang
    Thu Dec 6, 2012
    4:00 pm
    There is a good deal of resemblence of CR geometry in dimension three with conformal geometry in dimension four. Exploiting this resemblence is quite fruitful. For instance, the presence of several conformally covariant operators in both geometries allows us to formulate correct conditions for the embedding problem as well as the CR Yamabe problem...
  • Mitchell Luskin
    Thu Nov 15, 2012
    4:00 pm
    Many materials problems require the accuracy of atomistic modeling in small regions, such as the neighborhood of a crack tip. However, these localized defects typically interact through long ranged elastic fields with a much larger region that cannot be computed atomistically. Many methods have recently been proposed to compute solutions to these...
  • Professor Mei-chi Shaw
    Thu May 24, 2012
    4:00 pm
      The Cauchy-Riemann operator for domains in a complex manifold is well understood for domains in complex spaces. However, much less is known for the solvability and regularity for the Cauchy-Riemann operator in a complex manifold which is not complex spaces  or Stein. Recently, some progress has been made for the L2...
  • George Papanicolaou
    Mon Apr 23, 2012
    4:00 pm
    I will review briefly some recent developments in financial mathematics research, put them in a historical context, and then discuss the modeling and analysis of systemic risk phenomena.