Title: Finding soap films in non-Euclidean geometry Abstract: In many computer graphics applications we approximate a smooth surface with one made up of tiny triangles. A common problem is to determine which way to move the vertices (the corners of the triangles), so that the total surface area decreases. If the boundary of the surface […]
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, A.V. Hill observed muscles heat when they contract, but not when they relax. Based on experiments on frogs he posited a mathematical description of skeletal […]
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 some special cases it forms a ring. In this talk, we will discuss this phenomenon in Commutative Algebra. In particular, we will talk about the […]
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 novel approach which combines a density-based metric with graph-based clustering. This density-based path metric allows for fast algorithms and strong theoretical guarantees when clusters concentrate […]
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 can play to help "see" different properties. These puzzling games can be used to provide insight into deeper mathematical content as well. Time permitting, we […]
