Each year the Department of Mathematical Sciences holds a special lecture in honor of Professor Richard C. DiPrima, who was a professor in the Math Sciences Department and started as chair of the department in 1972.
Abstract: It is cliché to mimic biological design rules in synthetic materials, yet this is the precise challenge for regenerative medicine, therapies for disease pathologies, and vaccines. To design and engineer solutions to biological dysfunction, it is essential to understand Nature’s design rules for successful function. Today, we have data, amazing data, from advances in super-resolution (spatial and temporal) microscopy, targeted fluorescent signaling, chemical synthesis, and various passive and active probes of living systems. I will introduce two biological systems that rely on transient, short-lived, binding interactions to perform diverse functionalities: the genome in live cells with the requirement of genes to self-organize; and, the mucus barriers covering every organ with the requirement to regulate diffusive transport of foreign species within and to flow in order to clear all trapped insults. Time permitting, I will mention other examples. Each system is explored through feedback between experimental data, data analytics, mechanistic modeling and computation, and visualization of experimental and simulated data. Many collaborators will be acknowledged in the lecture.
What is a random function? What is noise? The standard answers are nonsmooth, defined pointwise via the Wiener process and Brownian motion.
Chebfun starts from the idea of continuous analogues of Matlab operations: vectors are overloaded to functions and matrices to operators. The result is a beautiful tool for all kinds of problems of rootfinding, quadrature, optimization, and ODEs.
Abstract: As events of the past decade have tragically demonstrated, tsunamis pose a major risk to coastal populations around the world. Numerical modeling is an important tool in better understanding past tsunamis and their geophysical sources, in real-time warning and evacuation, and in assessing hazards and mitigating the risk of future tsunamis. I will discuss a variety of techniques from adaptive mesh refinement to probabilistic hazard analysis that are being used for tsunamis and related geophysical hazards.
The range of shapes in the plant (and animal) world is "enough to drive even the sanest man mad", wrote Darwin. Motivated by qualitative and quantitative biological observations, I will show that there is a "method in the madness" - using examples of growth and form in tissues and organs such as the undulating fringes on a leaf, the looping of your gut, and the convolutions in your brain. In each case, we will see how a combination of biological and physical experiments, mathematical models and computations allow us to unravel the quantitative basis for the diversity and complexity of biological form, while creating new subjects of study in geometry, analysis and statistics.