
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, almostperiodic operators. I will consider two types of results:
1. BetheSommerfeld 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 BurnsSpatzier provides a link between irreducible symmetric spaces of noncompact 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 Meichi Shaw
Thu May 24, 2012
4:00 pm
The CauchyRiemann 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 CauchyRiemann 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.