The next Analysis and PDE seminar will take place Monday, October 15, from 4-5pm in 740 Evans.

Title: The effect of threshold energy obstructions on the $L^1 \to L^\infty$

dispersive estimates for some SchrÃ¶dinger type equations

Abstract: In this talk, I will discuss the differential equation $iu_t

= Hu, H := H_0 + V$ , where $V$ is a decaying potential and $H_0$ is a

Laplacian related operator. In particular, I will focus on when $H_0$

is Laplacian, Bilaplacian and Dirac operators. I will discuss how the

threshold energy obstructions, eigenvalues and resonances, effect the

$L^1 \to L^\infty$ behavior of $e^{itH} P_{ac} (H)$. The threshold

obstructions are known as the distributional solutions of $H\psi = 0$

in certain dimension dependent spaces. Due to its unwanted effects on

the dispersive estimates, its absence have been assumed in many

work. I will mention our previous results on Dirac operator and recent

results on Bilaplacian operator under different assumptions on

threshold energy obstructions.