Topology Seminar

Equivariant multiplicative infinite loop space theory is interesting, but hard. I will describe definitions in terms of symmetric groups which promise to give an easy new way to build the theory. As I shall describe, the main obstruction to making the new theory rigorous is the elementary categorical combinatorics of symmetric groups.

I will give an overview of time series data (that is, data sampled at different points in time) and spatially autocorrelated data (e.g., home prices, where the price of the house next to yours contains information about the likely price of your house). I'll then discuss the most common statistical models for such data, including ARIMA models that factor in what the past knows about the present, spectral models based on Fourier analysis, spatially weighted models, and the general linear mixed model for data with both spatial and temporal autocorrelation. I'll illustrate these models with vignettes from my research, on problems related to drug overdose and to the policing of protests in the USA. If there is time, I will explain some new research applying topological data analysis (TDA) to model the spatiotemporal spread of overdoses.