Abstract: I will overview the following different wave phenomena in integrable nonlinear wave equations: (1) universal patterns in the dynamics of fluxon condensates in the semi-classical limit; (2) modulational instability of periodic travelling waves; (3) rogue waves on the background of periodic and double-periodic waves. Main examples include the sine-Gordon equation, the nonlinear […]
Title: Our muscles aren't one-dimensional fibres. Abstract: Skeletal muscles possess rather amazing mechanical properties. They possess an intricate structure, and behave nonlinearly in response to mechanical stresses. In the 1910s, […]
Abstract: The system of shallow water equations and related models are widely used in oceanography to model hazardous phenomena such as tsunamis and storm surges. Unfortunately, the inherent uncertainties in […]
Title: An ideal convergence: an example in noncommutative metric geometry Abstract: The ability to calculate the distance between sets (rather than just distance between points) has found applications in geometry […]
Title: How do zebrafish get their stripes — or spots? Abstract: Many natural and social systems involve individual agents coming together to create group dynamics, whether the agents are drivers […]
In this talk, we present reduced order models (ROMs) for turbulent flows, which are constructed by using ideas from large eddy simulation (LES) and variational multiscale (VMS) methods. First, we […]
Title: Groups, Graphs and Trees Abstract: What do we mean by the geometry of a group? Groups seem like very abstract objects when we first study them, and it's natural […]
Abstract: Classification is a fundamental task in data science and machine learning, and in the past ten years there have been significant improvements on classification tasks (e.g. via deep learning). […]
Title: Trace Ideals and Endomorphism Rings Abstract: In many branches of mathematics, the full set of "functions" between two objects exhibits remarkable structure; it often forms a group and in […]
Abstract: This talk discusses multiple methods for clustering high-dimensional data, and explores the delicate balance between utilizing data density and data geometry. I will first present path-based spectral clustering, a […]
Title: Puzzling Permutations Abstract: Permutations are one of the most fundamental notions in mathematics. In this talk, we will discuss a visual representation of permutations and introduce some games one […]
Given a homogeneous multilinear polynomial F(x) in n variables with integer coefficients, we obtain some sufficient conditions for it to represent all the integers. Further, we derive effective results, establishing […]
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