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Dr. Richard Hammack

Title: Integrate THIS: the mathematics of planimeters

Abstract: A planimeter is a mechanical analog device that evaluates definite integrals. A typical planimeter features a dial and a stylus attached to an arm. As the stylus traverses the boundary of a region, the dial reads off the enclosed area. Planimeters have been mostly forgotten since the advent of computers, but at one time they were fairly commonplace.

I will explain the history and mathematics of planimeters, and I will demonstrate one that I made from two pieces of cast-off junk. It has only one moving part, but it can evaluate any definite integral that it can reach.

Bio:Richard Hammack is a professor of mathematics at Virginia Commonwealth University. He holds a B.F.A in painting from Rhode Island School of Design, a M.S. in computer science from VCU and a Ph.D in mathematics from UNC Chapel Hill. Prior to VCU, he taught at UNC, Wake Forest University and Randolph-Macon College.

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Dr. Igor Erovenko

Title: A glimpse into behavioral epidemiology: How dynamic human behavior affects the COVID-19 pandemic

Abstract: The COVID-19 pandemic has caused more than 90 million cases and 2 million deaths worldwide to date. No therapeutic drugs are currently available for this novel coronavirus, and vaccines approved for emergency use are only starting to become available. Most measures to prevent the spread of COVID-19 are thus based on reducing contact between infected and susceptible individuals. Most of these measures such as quarantine and self-isolation require voluntary compliance by the population. Yet humans may act in their (perceived) self-interest only. We construct a mathematical model of COVID-19 transmission coupled with a dynamic game model of adaptive human behavior. We model the social evolution of human behavior using imitation dynamics. Individuals adopt certain behavioral strategies and periodically revise their strategies by imitating the strategies of other (more successful) individuals. Individuals inform their strategic choices based on perceived prevalence and burden of the disease and sensitivity to isolation measures. This results in complex interplay between the epidemiological model, which affects success of different strategies, and the game-theoretic behavioral model, which in turn affects the spread of the disease. Our main findings demonstrate that the second wave of the pandemic, which has been observed in the US, can be attributed to rational behavior of susceptible individuals, and that multiple waves of the pandemic are possible if the rate of social learning of infected individuals is sufficiently high.

Bio: Dr. Igor Erovenko is an Associate Professor and Associate Head in the Department of Mathematics and Statistics at UNC Greensboro. He received his PhD in mathematics from the University of Virginia in 2002 and has been a faculty member at UNC Greensboro since then. His current research interests lie in the field of mathematical biology in general and evolutionary game theory in particular. Dr. Erovenko actively involves students in his research, and he supervised completed research projects of 23 undergraduate students to date. He is passionate about various outreach activities, and in 2020 he founded a Mathematics Flipped brand, which includes a YouTube channel with educational mathematical videos, a blog and a Twitter account.

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