Title: Stabilization rates for the damped wave equation with polynomial and oscillatory damping Abstract: In this talk I will discuss energy decay of solutions of the Damped wave equation. After giving an overview of classical results I'll focus on the

Conformal invariance of percolation on random planar maps Conformal invariance of critical percolation on the triangular lattice was proved by Smirnov. His proof is hard to extend to critical percolation on other lattices since his proof relies on a combinatorial

Title: A bulk gap in the presence of edge states for a HaldanepseudopotentialAbstract: In this talk, we discuss a recent result on a bulk gap for atruncated Haldane pseudopotential with maximal half filling, whichdescribes a strongly correlated system of spinless

Title: A Fredholm approach to scattering Abstract: We will give a friendly introduction to the scattering theory, specifically to the matrix for Schrodinger operators.  We will then discuss how a new functional analytic approach to analysis of non-elliptic equations, due to

Title - Propagation of singularities in subelliptic PDEs Abstract - In this talk, we consider the wave equation where the Laplacian is replaced by a sub-Laplacian (also called ``Hörmander sum of square''), which is an hypoelliptic operator. We handle the

Title: Fourier optimization, prime gaps, and zeta zeros Abstract: There are many situations where one imposes certain conditions on a function and its Fourier transform and then wants to optimize a certain quantity. I will describe two ways these types of Fourier optimization problems can arise in the context of the explicit

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

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

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

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