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UWaterloo Applied Math PhD Candidate Dongze Li discusses High-order provably-stable scheme on space-time curvilinear coordinates with shock-tracking capability. 

Parallel-in-time methods such as multigrid-reduction-in-time (MGRIT) and parareal utilize an iterative multilevel multigrid structure to solve linear systems of differential equations by solving a coarse-grid problem, which is less costly while also approximating the original, fine-grid problem. Such methods have been successfully applied to speeding up the solution of parabolic PDEs.

Complex systems consist of a collection of devices with local dynamics and control that are coupled by physical or cyber networks. Examples include the electrical power grid, communication systems, and networks of mobile robots and autonomous vehicles. Such systems provide essential services to society but are notoriously challenging to analyze or control due to their large scale and complexity. The talk will discuss new methods to enable safe, reliable, and desired operation of complex systems.

The theory of non-regular separation is examined in its geometric form and applied to the bi-Helmholtz equation in the flat coordinate systems in 2-dimensions. It is shown that the bi-Helmholtz equation does not admit regular separation in any dimensions on any Riemannian manifold.

This research proposal explores the role of Poisson-Lie and quantum group symmetries in gravity and physics. We review the previously established appearances of Poisson-Lie symmetries (the semi-classical picture of quantum group symmetries) and quantum group symmetries in 3D gravity as well as our novel advancements in elucidating such structures in 4D gravity.

The human heart is a complex system that can undergo a critical transition to an abnormal rhythm, known as a cardiac arrhythmia. How to predict or assess the risk of cardiac arrhythmia in individual patients with heart disease is not clear. In this talk, Dr. Thomas Bury will demonstrate how deep learning can be combined with mathematical models of the heart to (i) improve prediction of an arrhythmia known as alternans, and (ii) discover mechanisms that can lead to arrhythmia.

Many aquatic environments are characterized by regions where water density varies over depth, often due to temperature or salinity gradients. These ‘pycnoclines’ are associated with intense biological activity and can affect carbon fluxes by slowing the descent of particles. We explore the effects of stratification on the fundamental hydrodynamics of settling particles, rising drops, and small organisms.

El Niño–Southern Oscillation (ENSO) is a climate phenomenon occurring every 3-7 years in the tropical Pacific. It is a pattern shifting between anomalous warm and cold events within equatorial Pacific, with irregularity in amplitude, duration, temporal evolution, and spatial structure. This research focuses on a specific ENSO model developed by Majda and coworkers, where state-dependent stochastic wind bursts and nonlinear advection of sea surface temperature are coupled to a simple ocean–atmosphere model that is otherwise deterministic, linear, and stable.

General Relativity is currently the most successful theory for our understanding of gravity and spacetime. Proposed by Albert Einstein more than 100 years ago, its predictions are still being proven accurate by cutting-edge experiments, exemplified by the detection of gravitational waves by LIGO in 2015 and the black hole picture obtained in 2022. However, there still is much to be understood when Quantum Physics comes into play. For years, many physicists have tried to obtain a complete theory of Quantum Gravity, but we still do not have one.