Department of Mathematics & Statistics Colloquia 2021/22
10/11/2021
Speaker: Dr Matthew Fayers, School of Mathematical Sciences, Queen Mary University of London
ABSTRACT:
The Mullineux map is a function on partitions which arises in the representation theory of the symmetric group. The Mullineux problem is to describe this function purely combinatorially. I will describe the background and the history of this problem and explain the known combinatorial solutions, and then talk about a new solution based on crystals and regularisation.
17/11/2021
Title: John--Nirenberg spaces revisited
Speaker: Dr Oscar Dominguez Bonilla, School of Mathematical Sciences, Complutense University of Madrid
ABSTRACT:
We study John—Nirenberg-type spaces where oscillations of functions are controlled via covering lemmas. Our methods give new surprising results and clarify classical inequalities. Joint work with Mario Milman (Florida and Buenos Aires).
24/11/2021
Speaker: Professor Jochen Einbeck, Department of Mathematical Sciences, Durham University, UK
ABSTRACT:
Count data are usually fitted through Poisson models or simple two-parameter models such as the Negative Binomial distribution. Whilst a range of numeric methods and statistical tests do exist for assessing or comparing model fit in this context, diagrammatic methods are few. We present here a diagnostic plot, which we refer to as a `Quantile Band plot', that may be used to visually assess the suitability of a given count regression model. In the case of diagnosed model inadequacy, the plot has the unique feature of conveying precise information on the character of the violation, hence pointing the data analyst towards a potentially better model choice. The graphical tool is illustrated by means of data examples from biological dosimetry, where counts of chromosome aberrations or protein foci from blood samples are used to infer the contracted radiation dose following exposure to ionizing radiation (joint work with Paul Wilson).
01/12/2021
Title: The changing populations and economic fortunes of small places in the United States
Speaker: Dr Dylan Connor, School of Geographical Sciences & Urban Planning, Arizona State University
ABSTRACT:
The growing importance of urban areas in the economic geography of the United States has led to concerns that rural dwellers are facing newfound hardship. According to this dominant view, once prosperous rural communities have struggled to gain a foothold in an economy that increasingly favors the large coastal cities at the core of today’s leading economic sectors. Distressed communities are cited as evidence of the demise of rural America and as an explanation for the rejuvenation of rural conservative politics. But is this an accurate reflection of the changes unfolding across rural places? We argue that the narrative of rural impoverishment certainly holds for many rural places, but is a poor fit for others. We establish this fact by developing and applying cutting-edge methods in spatial demography and sequence analysis to examine change across all rural places in the lower 48 states from 1980 to 2018. Our findings reveal that rural change can be characterized by eleven distinct trajectories, varying from sharp increases in local poverty to more stable levels of prosperity, with varying trajectories of demographic change. We also establish the importance of these changes for intergenerational mobility: in communities where poverty is entrenched or where conditions have worsened, children’s life chances are more uncertain. This more nuanced understanding of the circumstances facing rural communities is essential to address the widening disparities between urban and rural places. Furthermore, our analytical framework provides a template for studying contextual change across a wide range of places, countries and contexts over time.