Mathematical Colloquium

In 1902 Burnside asked whether any finitely generated torsion group is necessarily finite. By now there is a long line of negative answers, albeit not necessarily accessible. I will explain the basics of small cancellation theory and our approach to the Burnside problem.
(j/w A. Atkarskaya and E. Rips)

Accurate and timely inversion of tsunami source parameters from observational data is essential for developing effective early warning systems, where decisions must be made under uncertainty. The detection of tsunami sources from observational data, such as buoy and hydrophone measurements, poses significant challenges in Bayesian inverse modeling. The forward problem involves solving complex hyperbolic systems, often modeled using the shallow water equations.
I will discuss the discretization of the forward model using an ADER-DG method, which is capable of handling wetting and drying processes. Additionally, I will outline how to efficiently perform the inversion using a fully parallelized multi-level Markov Chain Monte Carlo (MLMCMC) method. A key challenge lies in balancing computational feasibility with accuracy, particularly in high-dimensional parameter spaces. To address this, I will demonstrate the effect of incorporating a Gaussian Process surrogate model as a computationally inexpensive coarse-level approximation.

TBA

TBA