while Ivana watches “My Love from the Star“… “The” star? Which star?
This list of links is mainly for my future reading. It’s roughly a list of future research directions that I might want to consider.
Applications of Sheaves
First off, there’s Ghrist and his topological sensing. But I want to focus on other groups doing applied sheaf theory.
M. Robinson also works on Inverse Problems.
UW has an REU this year on inverse problems. Their reading list looks like a good place to start.
Inverse Problems for Undergraduates also looks like a book that I might want to browse through in the school library.
I think it’s safe to say that practically everyone working in this area was gathered at IMA’s conference on Topological Systems: Communication, Sensing and Actuation. I’ve seen some of it before (the usual contenders), but it’ll take me a while to really look through all of this.
Distributed, Multi-agent Systems
I’m especially interested in directions motivated by statistical mechanics. Phase transitions and universality seem interesting. Here’s a great article from Quanta magazine about universality: In Mysterious Patterns, Math and Nature Converge.
Emergence, of which flocking is a popular example, is also interesting. Smale has an article about The Mathematics of Emergence.
The emergence article makes use of the Laplacian, which also features prominently in message-passing and gossip algorithms. The Simons Foundation has an article about the Laplacian and algorithms related to it. In fact, Quanta magazine (published by the SImons Foundation) has pretty good articles on related areas. They make math sexy!
Categorified Network Theory
John Baez’s This Week’s Finds and Azimuth blog also make math sexy. But there’s too much stuff to fit into this tiny list. I’ll just highlight his Network Theory series. Some of the topics it touches on include information theory and Bayesian networks.
Ok that’s enough gleaning for today. Time to digest the articles I’ve gathered, and decide if there’s some common underlying direction that can serve as my compass through grad school. Hopefully the harvesters that have come before me haven’t cleared these fields of interesting problems.