Thu Apr 25, 2013
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")...
Thu Apr 4, 2013
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...
Thu Jan 17, 2013
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...
Thu Dec 6, 2012
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...
Thu Nov 15, 2012
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
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...
Mon Apr 23, 2012
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.