Hardy inequalities for simply connected planar domains

Speaker: 

Alexander Sobolev

Institution: 

University of Birmingham, UK

Time: 

Thursday, April 6, 2006 - 2:00pm

Location: 

MSTB 254

In 1986 A. Ancona showed, using the Koebe one-quarter Theorem, that for a simply-connected planar domain the constant in the Hardy inequality with the distance to the boundary is greater than or equal to 1/16. We consider classes of domains for which there is a stronger version of the Koebe Theorem. This implies better estimates for the constant appearing in the Hardy inequality.

Random difference equations with Markov-dependent coefficients

Speaker: 

Professor Alex Roiterstein

Institution: 

University of British Columbia

Time: 

Tuesday, April 18, 2006 - 11:00am

Location: 

MSTB 254

For a class of stationary Markov-dependent sequences
(A_n,B_n)
in R^2, we consider the random linear recursion S_n=A_n+B_n
S_{n-1}, n \in \zz, and show that the distribution tail of its
stationary solution has a power law decay.

The spectrum of the weakly perturbed Landau Hamiltonian

Speaker: 

Alexander Pushnitski

Institution: 

King's College, London, visiting Caltech

Time: 

Thursday, April 20, 2006 - 2:00pm

Location: 

MSTB 254

The subject of the talk is the spectrum of a two-dimensional
Schrodinger operator with constant magnetic field and a compactly supported electric potential. The eigenvalues of such an operator form clusters around the Landau levels.
The eigenvalues in these clusters accumulate towards the Landau levels super-exponentially fast. It appears that these eigenvalues can be related to a certain sequence of orthogonal polynomials in the complex domain. This allows one to accurately describe the rate of accumulation of eigenvalues towards the Landau levels. This description involves the logarithmic capacity of the support of the electric potential. The talk is based on a joint work with Nikolai FIlonov from St.Petersburg.

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