## Imaging and Computing Seminar

### Yajun Zhou , Chemistry, Harvard

**Title:**

Robust Solution to Integral Equations via Topological
Compactness: Applications in Chemical Kinetics and Electromagnetic
Scattering

**Abstract:**

We study the inverse Laplace problem in chemical kinetics
and the vector wave scattering problem in dielectric optics. We point
out that topological compactness plays an essential role in the
robust solutions to the integral equations associated with the two
problems under investigation. By exploiting the $ w^*$-compactness
theorem of Banach-Alaoglu, we devise a numerically stable method to
extract the probability distribution of kinetic rate constants from
noisy measurements in the time domain. By constructing a compact
operator $\hat {\mathcal G}+2\hat{\mathcal G}^2 $ from the non-compact
Green operator $\hat{\mathcal G} $ of light scattering, we demonstrate
robust solutions to the scattering of electromagnetic waves on
non-accretive homogeneous dielectric media, except for a critical
susceptibility value $ \chi=\epsilon_r-1=-2$ that is independent of
the dielectric shape.