The asymptotic shift for the principal eigenvalue under small obstacles.

Speaker: 

Professor Iddo Ben-Ari

Institution: 

UCI

Time: 

Tuesday, October 4, 2005 - 11:00am

Location: 

MSTB 254

We study the asymptotic shift for principal eigenvalue for a
large class of second order elliptic operators on bounded domains subject
to perturbations known as obstacles. The results extend the well-studied
self-adjoint case. The approach is probabilistic.

Speaker: 

Time: 

Saturday, October 29, 2005 - 10:00am

Location: 

MSTB 118

Southern California Number Theory Day

Estimates for the tangential Cauchy-Riemann equations with minimal smoothness

Speaker: 

Professor Meichi Shaw

Institution: 

Notre Dame

Time: 

Thursday, September 29, 2005 - 4:00pm

Location: 

MSTB 254

We study the regularity for the tangential Cauchy-Riemann equations and the associated Laplacian on CR manifolds with minimal smoothness assumption. One application is to extend the embedding theorem of Boutet De Monvel
to strongly pseudoconvex CR manifolds of class C^2.

(Joint work with Lihe Wang).

Special Lagrangian T^2-cones in C^3

Speaker: 

Emma Camberry

Institution: 

MSRI

Time: 

Tuesday, April 13, 2004 - 4:00pm

Location: 

MSTB 254

Special Lagrangian 3-folds are of interest in mirror symmetry, and in particular play an important role in the SYZ conjecture. One wishes to understand the singularities that can develop in families of these 3-folds; the relevant local model is provided by special Lagrangian cones in complex 3-space. When the link of the cone is a torus, there is a natural invariant g associated to the cone, namely the genus of its spectral curve. We show that for each g there are countably many real (g-2)-dimensional families of such special Lagrangian cones.

One direction and one component regularity for the Navier-Stokes equations

Speaker: 

Professor Igor Kukavica

Institution: 

USC

Time: 

Thursday, November 17, 2005 - 4:00pm

Location: 

MSTB 254

We consider sufficient conditions for regularity of weak solutions of the Navier-Stokes equation. By a result of Neustupa and Panel, the weak solutions are regular provided a single component of the velocity is bounded. In this talk we will survey existing and present new results on one component and one direction regularity.

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