Title: Modeling and analysis of localized vegetation patterns on curved topography Abstract: We propose a two-component reaction-advection-diffusion model for vegetation density and soil water concentration on a curved terrain which accounts for downhill flow of soil water, spatially dependent effective evaporation of soil water, and vertical rainfall on a curved surface. In the limit of slow diffusion of vegetation, we construct a one-spot localized solution corresponding to one patch of a periodic spotted vegetation pattern. We derive an ODE for the motion…

Title: Asymptotic Analysis of the Interaction Between a Soliton and a Regular Gas of Solitons (a.k.a. Gulliver and the Lilliputians) Abstract: N. Zabusky coined the word "soliton" in 1965 to describe a curious feature he and M. Kruskal observed in their numerical simulations of the initial-value problem for a simple nonlinear PDE. The first part of the talk will be a broad introduction to the theory of solitons/solitary waves and integrable PDEs (the KdV and modified KdV equation in particular),…

Title:  Energy Minimizing Surface Tension Configurations for Microparticles Abstract: An important area of microfluidics is the creation and manipulation of small droplets. This is commonly done using microchannels or electrowetting. Recently a new method is proposed to create templated droplets using amphiphilic microparticles. These particles are observed to hold nearly equal volumes of aqueous liquid when dispersed in an oil–water mixture. However a theory for this behavior is lacking. In this paper, we present a mathematical model based on minimizing the…

Title: Eigenfunction restriction estimates on curves with nonvanishing geodesic curvatures Abstract: Studying eigenfunctions of the Laplace-Beltrami operator on compact Riemannian manifolds (without boundary) is one of the interesting topics in Harmonic Analysis. One way to study them is to consider the L^p estimates of the eigenfunctions restricted to submanifolds. In this talk, we briefly summarize previous results and would like to talk about the logarithmic improved analogue for the restriction to curves with nonvanishing geodesic curvatures, in the presence of nonpositive…

Title: Equispaced Fourier representations for efficient Gaussian process regression from a billion data pointsAbstract: Gaussian process regression is widely used in geostatistics, time-series analysis, and machine learning. It infers an unknown continuous function in a principled fashion from noisy measurements at $N$ scattered data points.  The prior on the function is Gaussian, with covariance given by some user-chosen translationally invariantkernel.  Yet $N$ has been limited to about $10^6$, even with modern low-rank methods.  Focusing on low spatial dimension (1--3), we present…

Title + Abstract: TBD The Dalhousie-AARMS Analysis-Applied Math-Physics Seminar takes place on Fridays from 4 - 5 pm Atlantic Time over either Zoom and/or in Chase 227 depending on the speaker.  If you would like to attend, please email the organizers for connection details.

Title + Abstract: TBD The Dalhousie-AARMS Analysis-Applied Math-Physics Seminar takes place on Fridays from 4 - 5 pm Atlantic Time over either Zoom and/or in Chase 227 depending on the speaker.  If you would like to attend, please email the organizers for connection details.

Title: Universality limits for orthogonal polynomialsAbstract: It is often expected that the local statistical behavior ofeigenvalues of some system depends only on its local properties; forinstance, the local distribution of zeros of orthogonal polynomials shoulddepend only on the local properties of the measure of orthogonality. Thisphenomenon is studied using an object called the Christoffel-Darbouxkernel. The most commonly studied case is known as bulk universality,where the rescaled limit of Christoffel-Darboux kernels converges to thesine kernel.In this talk, we will survey this…