Welcome to MATH-690!
Course name: Topics in Probability
More specifically: Topics in Random Topology
Instructor: Omer Bobrowski
Office: Physics building #108
Office hours: By appointment
In this course we will review recent advances in the interface between probability and topology. Most if not all of these topics can be viewed as generalizing classical results in probability (such as random graphs, percolation, coverage, random walks and spectral graph theory), for which we will provide some background as well. The main topics that will be covered are:
· Random combinatorial complexes (extensions of Erdős–Rényi random graphs)
· Random geometric complexes (extensions of random geometric graphs)
· Random walks on simplicial complexes (extensions of random walks on graphs)
Some background in topology and/or algebraic topology would be helpful, but is not required to take this course.
Each registered student will choose a relevant topic/paper to study, and present it in class at the end of the semester.