Department of

Mathematics


Seminar Calendar
for events the day of Wednesday, November 29, 2017.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Wednesday, November 29, 2017

3:00 pm in 243 Altgeld Hall,Wednesday, November 29, 2017

Minimal mathematical models of human and animal dynamical systems

Sara Clifton (UIUC and University of Idaho)

Abstract: Minimal mathematical models are used to understand complex phenomena in the physical, biological, and social sciences. This modeling philosophy never claims, nor even attempts, to fully capture the mechanisms underlying the phenomena, and instead offers insights and predictions not otherwise possible. Here, we build and explore minimal dynamical systems models to understand three complex animal and human systems. First, we incorporate the assumptions of Zahavi's handicap principle into a mathematical model of ornament evolution and show that this existing hypothesis is sufficient to explain the previously puzzling observation of bimodally distributed ornament sizes in a variety of species. Second, we propose a 'return-to-setpoint' model of chronic pain dynamics in sickle cell disease patients with the goal of offering personalized, data-driven recommendations for treating chronic pain. Third, we present a conceptual model of restaurant competition that predicts the existence of a critical gratuity rate threshold at which restaurant owners will disallow tipping to maximize their profits. Because of their simplicity, these models of complex human and animal systems offer new connections between existing ideas, give optimized solutions with limited data, and provide qualitative predictions of future events.

4:00 pm in 245 Altgeld Hall,Wednesday, November 29, 2017

Randomness in number theory

Junxian Li (UIUC Math)

Abstract: Given an integer, how many prime factors does it have? Does it have an even or odd number of prime factors? It turns out that these deterministic arithmetic functions behave like randomly distributed variables. In this talk, we will give examples of various distributions of number theoretic functions and show how randomness plays a role in number theory.