Summer Lectures

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In this talk, I will present 4 simple but useful applied math techniques in our lives. These projects were tackled in collaboration with undergraduate and graduate students. First, I will talk about the flight stability of objects, specifically cones and wedges. I will continue to talk about a simple deep learning technique in neuroscience and apply it to the Hodgkin-Huxley model. For the third project, I will present how asymptotic analysis can reduce a complex model for a tissue engineering scaffold pore. Finally, I will go over the mathematical modeling and simulation of a droplet or film on a wall by using the immersed boundary method.

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Giving several examples, I will explain what inverse (sometimes also called parameter estimation) problems are. I will demonstrate the main mathematical challenges, and discuss how they can be addressed.

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Why fish swim together in schools and why birds fly in flocks are enduring mysteries. These biological phenomena inspire interesting physics questions about interactions through fluid flows. This talk will focus on what we've learned in Courant's Applied Math Lab (AML) about the fluid dynamics of collective locomotion. We'll discuss lab experiments on "mock flocks" of robotic flyers and math models of the same that are simplified but highly effective. Flow interactions prove to have a Jekyll-and-Hyde personality: They can help to organize the members into orderly positions, but they also disrupt such formations through a new type of traveling wave.