Abstract: The Landau-de Gennes theory is a type of continuum theory that describes nematic liquid crystal configurations in the framework of the Q-tensor order parameter. In the free energy, there is a singular bulk potential which is considered as a natural enforcement of a physical constraint on the eigenvalues of symmetric, traceless Q-tensors. In this […]
Title: Spectral gap in random regular graphs and hypergraphs Abstract: Random graphs and hypergraphs have been used for decades to model large-scale networks, from biological, to electrical, and to social. Various random graphs (and their not-so-random properties) have been connected to algorithms solving problems from community detection to matrix completion, coding theory, and various other […]
Abstract The COVID-19 pandemic illustrates the importance of treatment-related decision making in populations. This article considers the case where the transmission rate of the disease as well as the efficiency […]
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 […]
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) […]
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 the system will inevitably damage the credibility of decision-making based on the deterministic model. The stochastic Galerkin (SG) method seeks a solution by applying the […]
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 and group theory as well as various branches of applied mathematics. The Hausdorff distance and the Gromov-Hausdorff distance are standard distances used in these applications. […]
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 a traffic jam, voters in an election, or locusts in a swarm. Self-organization also occurs at much smaller scales in biology, though, and here […]
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 give a general introduction to reduced order modeling and emphasize the connection to classical Galerkin methods (e.g., the finite element method) and the central role […]
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 to ask whether we can visualize them in some way. Given a group with a finite set of generators and relators, I will describe a […]
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