Summer Lectures

Synopsis:

Synopsis:

There are two rotary motors in biology, ATP synthase and the bacterial
flagellar motor.  Both are driven by transmembrane ionic currents.  
We consider an idealized model of such a motor, essentially an
electrostatic turbine.  The equations of the model are solved
explicitly to determine the electromechanical properties of the motor,
which turn out to obey the Onsager reciprocal relations of
non-equilibrium thermodynamics.  A design problem is formulated and
solved, and the optimal efficiency of the motor is evaluated.

Slides are available online:  
https://math.nyu.edu/~peskin/rotary_motor_ubc_talk.pdf

Synopsis:

The most recent Intergovernmental Panel on Climate Change Assessment Report (IPCC-AR6) states that "It is unequivocal that human influence has warmed the atmosphere, ocean and land." In this talk, we will explore the science behind this statement. We will take a tour through a hierarchy of climate models ranging from simplistic conceptual models of the greenhouse effect to complex computer simulations currently used for the IPCC reports, all predicting global warming is real and quantifiable. Our tour of history will also make clear the important contribution of Suki Manabe in the prediction of global warming, which won him the Nobel prize in 2021.

Synopsis:

In this talk, I will give an introduction to scientific writing and the publication process. Questions to be answered include: why publish? How do we write good manuscripts? Are some journals "better" than others? How does the peer review process work? And how can we make our results clear and interesting to a wide audience?

Synopsis:

In order to achieve practical quantum computation it is essential to design quantum logic gates that are high-fidelity and reliable. In this talk we’ll take a look at how to construct microwave/laser pulses to realize a user-specified quantum logic gate by solving an optimal control problem in which the state of the system is governed by the Schrödinger equation.

Synopsis:

This talk will discuss how the mathematical theory of optimal transport provides a natural framework for posing and answering questions related to data analysis and conditional probability distributions. Instances include determining and simulating such distributions from sparse data, discovering hidden factors that explain observed variability and consolidating multiple data sets.

Synopsis:

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.

Synopsis:

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.

Synopsis:

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.