Applied Math Seminar

Title: Designing Robust Networks of Coupled Phase Oscillators with Applications to the High-Voltage Electric Grid Abstract: A network is any collection of objects, called nodes, in which some pairs of these objects are connected by links, called edges. In a network of coupled phase-oscillators, each node represents a phase-angle (or an angle with periodicity) whose […]

Title: Renormalization and wild attractors for Fibonacci maps Abstract: A Fibonacci map is a piecewise defined map of a subset of an interval I onto I with a unique critical point of order d whose orbit undergoes nearest returns at Fibonacci times. It has been shown by Bruin, Keller, Nowicki and van Strien that such […]

Title: Smooth non-decaying solutions to the 2D dissipative quasi-geostrophic equations Abstract: In this talk we explore the two-dimensional dissipative surface quasi-geostrophic (SQG) equation with fractional diffusion of order 2α for α ∈ (1/2,1], focusing on the setting where the initial data does not decay at spatial infinity and periodicity is not assumed. In geophysical applications, […]

Title: Bi-Lipschitz Invariants Abstract: Consider a finite-dimensional real vector space and a finite group acting unitarily on it. We investigate the general problem of constructing Euclidean stable embeddings of the quotient space of orbits. Our embedding relies on subsets of sorted coorbits with respect to chosen window vectors. Our main injectivity results examine the conditions […]

Title: Do Taxes Affect Pre-Tax Income Inequality? Evidence from 100 Years of U.S. States Abstract: We study how U.S. state taxes have affected pre-tax income inequality during the last century. Our primary analysis focuses on the top marginal personal income and corporate income tax, and their effect on top incomes and top income shares within […]

Title: Learning on manifolds without manifold learning Abstract: Function approximation based on data drawn randomly from an unknown distribution is an important problem in machine learning. The manifold hypothesis assumes that the data is sampled from an unknown submanifold of a high dimensional Euclidean space. A great deal of research deals with obtaining information about […]

Title: Randomly pivoted Cholesky: Fast, accurate matrix approximation for scientific machine learning Abstract: Low-rank approximation of positive semidefinite matrices is a basic problem in computational mathematics, with many applications to machine learning and scientific computing. Existing approaches for this problem largely fall into two categories: simple, fast, but sometimes inaccurate methods and sophisticated, slower methods […]

Title: Erlang-Distributed SEIR Epidemical Models Abstract: We examine the effects of different dynamics in epidemiological models, focusing on two key approaches. The first model incorporates reaction-diffusion dynamics, where susceptible individuals avoid areas with high concentrations of infected individuals. The second model divides exposed and infectious individuals into symptomatic and asymptomatic subclasses. Our findings emphasize the […]

Title: Modeling viral STI epidemics Abstract: We will describe an SIR model of viral sexually transmitted infections in a population structured by sex and sexual preference and its validation in the simple SI case from HIV data incidence. We will also use the model to establish a plausible structure of the U.S. population by sexual […]

Title:    Randomized Kaczmarz Methods for Corrupted Tensor Linear Systems Abstract: Recovering tensor-valued signals from corrupted measurements is a central problem in various applications such as hyperspectral image reconstruction and medical imaging. This talk considers tensor linear systems of the form AX = B, that contain observations potentially affected by sparse, large-magnitude corruptions.  A quantile-based randomized […]

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