Applied Math Seminar

Title: Data science and applications in dynamic topic modeling Abstract: The shockwaves of the big data boom have thrown into sharp relief the critical need for domain-driven, large-scale data analytic techniques across the fields of, among others, finance, political science, economics, psychology, and medicine. It is not simply the size of data sets that contributes […]

Title: What is the best shape? Geometric problems arising in aggregation models Abstract: How do pair interactions shape the large-scale behaviour of a cloud of particles (animals, social agents ...) ?  In the most basic models, the shape of the cloud is determined by minimizing an attractive-repulsive interaction energy under suitable geometric constraints. When can […]

Title: Computational Approaches to Optimization Problems in Inhomogeneous Rods and Plates Abstract: In this talk, we will show the experiments of the vibration of plates to generate Chladni's figures and discuss computational approaches to optimization problems of inhomogeneous rods and plates. We consider both optimization of eigenvalues and localization of eigenfunctions. These problems are motivated by physical problems […]

Title: Understanding scientific fields with network analysis and topic modeling Abstract: As scientific disciplines get larger, it becomes impossible for an individual researcher to be familiar with the entire body of literature, which forces them to specialize in a sub-field. Such insulation can hinder the birth of ideas that arise from new connections, eventually slowing down […]

Title: Approximating Quasi-Stationary Distributions with Interacting Reinforced Markov Chains Abstract: An important question in ecology is what conditions must be met for a population of interacting species to coexist. In realistic models of such populations, after a large enough amount of time has passed, one or more of the species are sure to face extinction. […]

Title: Kolmogorov, Onsager and a Dyadic Model for Turbulence Abstract: We will briefly review Kolmogorov’s ( 41) theory of homogeneous turbulence and Onsager’s ( 49 ) conjecture that in 3-dimensional turbulent flows energy dissipation might exist even in the limit of vanishing viscosity. Although over the past 70 years there is a vast body of […]

Title: Mathematical modeling of polymerization processes in physiology Abstract: Polymerization, or aggregation, is essential for many physiological systems. For example, the emergence of a fibrin polymer mesh during the formation of a blood clot is required for a stable clot and long-term, sustained intracellular transport in neurons rely on persistent yet dynamic polymers that comprise the […]

Title: Randomized Sums of Graph Spectra Abstract: The adjacency matrix of an Erdős-Rényi-Gilbert graph is a random symmetric matrix whose entries are Bernoulli random variables. These entries, modulo the constraints imposed by symmetry, are independent. We aim to understand the asymptotic behavior of randomized sums of the spectra and singular spectra of these matrices. In […]

Title: Data-driven large eddy simulation of atmospheric turbulence Abstract: Over the last few years, machine learning has been critical in science and engineering and emerged as a data-driven turbulence model. However, machine learning depends on training data from previous experiments on turbulent flows. Typically, training data capture only a fraction of the active scales of […]

Title: Scattering Resonances Through Subwavelength Holes and Their Applications in Imaging and Sensing Abstract: The so-called extraordinary optical transmission (EOT) through metallic nanoholes has triggered extensive research in modern plasmonics and their applications in bio-sensing, imaging, etc. This talk aims to provide quantitative mathematical theories to understand a variety of resonances that induce the EOT […]

Title: Using Mutual Information of Hypergraph Compressions for Clustering Abstract: Hypergraphs are often used to represent higher order observed relationships between subjects of study. In particular, the vertices of a hypergraph could represent the basic elements of study, and edges represent observed relationships between the vertices. Implicitly, the assumption is that observed edges are more […]

Title:Geometric Scattering on Measure Spaces Abstract: Geometric Deep Learning is an emerging field of research that aims to extend the success of convolutional neural networks (CNNs) to data with non-Euclidean geometric structure. Despitebeing in its relative infancy, this field has already found great success in many applications such as recommender systems, computer graphics, and traffic […]