The topology of data

The paper that I wish to discuss today is An Introduction to Topological Data Analysis: fundamental and practical aspects for data scientists, by Frederic Chazal and Bertrand Michel. Topological data analysis is an exciting new field, and this paper can be understood by people from a wide range of backgrounds. Notation: For this paper, denotesContinue reading “The topology of data”

The science of going in circles on doughnuts

The paper that I’m going to be reviewing today is A Topological Look at the Quantum Hall Effect. It explains an amazing coming together of topology and quantum physics, of all things, and provides a review of very important, Nobel prize winning work in Physics. The Hall Effect We all learned in high school thatContinue reading “The science of going in circles on doughnuts”

Explaining the beginner’s problems with Topology

When one suddenly starts studying compactness and connectedness and other topological concepts in college, one is likely to get confused. Where did all these concepts come from? Then, seemingly intuitive properties of start being proven using these alien notions. Forming a big picture which includes these concepts seems difficult. One still thinks about the realContinue reading “Explaining the beginner’s problems with Topology”