The APDE seminar on Monday, 11/04 will be given by Jared Wunsch in Evans 939 from 4:10 to 5pm.

Title: A tale of two resolvent estimates

Abstract:
I will discuss two new results concerning the best of resolvent estimates and the worst of resolvent estimates.  In the former, case, that of nontrapping obstacles or metrics, we have obtained (in joint work with Galkowski and Spence) optimal, dynamically determined, constants in the standard non-trapping estimate for the (chopped off) resolvent.  In the latter case, that of obstacles or metrics that may have very strong trapping, I will discuss joint work with Lafontaine and Spence that shows the estimates to be a far, far better thing than you might have expected, provided you omit a small set of frequencies from consideration.

The APDE seminar on Monday, 10/28 will be given by Melissa Tacy in Evans 939 from 4:10 to 5pm.

Title: Adapting analysis/synthesis pairs to pseudodifferential operators

Abstract:
Many problems in harmonic analysis are resolved by producing
an analysis/synthesis of function spaces. For example the Fourier or
wavelet decompositions. In this talk I will discuss how to use Fourier
integral operators to adapt analysis/synthesis pairs (developed for the
constant coefficient PDE case) to the pseudodifferential setting. I will
demonstrate how adapting a wavelet decomposition can be used to prove
$L^{p}$ bounds for joint eigenfunctions.

The APDE seminar on Monday, 10/21 will be given by Benjamin Küster in Evans 939 from 4:10 to 5pm.

Title: Pollicott-Ruelle resonances and Betti numbers

Abstract:
In joint work with Tobias Weich, we study the multiplicity of
the Pollicott-Ruelle resonance 0 of the Lie derivative along the
geodesic vector field on the cosphere bundle of a closed negatively
curved Riemannian manifold, acting on flow-transversal one-forms. We
prove that if the manifold admits a metric of constant negative
curvature and the Riemannian metric is close to such a constant
curvature metric, then the considered resonance multiplicity agrees with
the first Betti number of the manifold, provided the latter does not
have dimension 3. In dimension 3 and for constant curvature, it turns
out that the resonance multiplicity is twice the first Betti number.

The APDE seminar on Monday, 10/07 will be given by Deng Zhang in Evans 939 from 4:10 to 5pm.

Title – The stochastic nonlinear Schrödinger equations: defocusing mass and energy critical cases

Abstract – In this talk we will present our recent results on stochastic nonlinear Schrödinger equations with linear multiplicative noise, particularly, in the defocusing mass-critical and energy-critical cases. More precisely, for general initial data, we obtain the global existence and uniqueness of solutions in both mass-critical and energy-critical case. When the quadratic variation of noise is globally bounded, we also prove the rescaled scattering behavior of stochastic solutions in the spaces L2, H1 as well as the pseudo-conformal space. Furthermore, the Stroock-Varadhan type theorem is derived for the topological support of solutions to stochastic nonlinear Schrödinger equations in the Strichartz and local smoothing spaces.