Random Points of Shapes in Space (Spring 2025)
A phrase that we encounter a lot as mathematicians is the phrase ``generate a random sample.'' There is usually more information that comes along with the phrase, such as a probability distribution, or a ``shape'' that the sample is said to be generated from. Regardless, it is not so obvious what is rigorously meant by this phrase. What is the mathematical definition of a random sample? At a more foundational level, what is random? In this project, we will be pondering these questions and more. It will start us off in the realm of probability theory and will take us into ideas of computational geometry. There we will ask related questions about how one could program a computer to generate random samples from a shape, and in what cases one is able to recover interesting properties of a shape by just investigating enough random samples of it.
For more information contact Enrique Alvarado (enrique3@iastate.edu)
People:
Enrique Alvarado (Postdoc)