Pertussis, commonly known as whooping cough, is caused by the bacterial pathogen Bordetella pertussis. Completely susceptible individuals experience severe disease, with the hallmark whooping cough, but those with partial immunity have milder, if any symptoms. Immunity following natural infection (or immunization) may wane, increasing susceptibility with time since exposure. In this talk, we begin by examining…

Students often take precalculus or college algebra as a terminal math course, leaving them with the impression that mathematics lacks real meaning. Due to the increasingly interdisciplinary nature of the mathematical sciences, we are well-poised to intervene and design inspiring general education courses that reveal the utility of mathematics. In this talk, I will share…

A circle packing is the mathematical name for a collection of circles. I am interested in circle packings with a fixed pattern of tangencies between the circles. Given a tangency pattern, one might ask questions like, "Can I find a circle packing with that tangency pattern?" and "How many such circle packings can I find?"…

In this demo, we will discover some interesting properties about symmetry by starting with some special transformation matrices. This talk will be a combination of interactive work with the material and some discussion of teaching strategies.

How could you design a stadium so that a rectangular playing field looks the same size to every spectator? What about for a circular wrestling ring? In this talk, we study these and related questions, which can all be viewed as generalizations of Thales' Theorem---that a line segment L in the plane "looks the same…

Experience suggests that uncertainties often play an important role in quantifying the performance of complex systems. Therefore, uncertainty needs to be treated as a core element in the modeling, simulation, and optimization of complex systems. In this talk, I will first present a review of the novel UQ techniques I developed to conduct stochastic simulations…

Principal component analysis (PCA) is a useful tool when trying to uncover factor models from historical asset returns. For the implied volatilities of U.S. equities there is a PCA-based model with a principal eigenportfolio whose return time series lies close to that of an overarching market factor. Specifically, this market factor is the index resulting…

Persistent homology is a key method in topological data analysis, a young but rapidly growing field at the intersection of computational geometry and algebraic topology. Persistence is used to describe the shape of data in a way that generalizes clustering: besides considering what connected components (clusters) are present in the data, it also describes their…

Many estimates in analysis  have certain “common structures” which makes it possible to obtain them with  what is now called Bellman function method. Originally the method appeared in control theory (stochastic or deterministic), however its systematic use  in harmonic analysis or probability started only recently  in works of Burkholder where he obtained the sharp constants…