Welcome to MATH-690!

 

Course name: Topics in Probability

More specifically: Topics in Random Topology

 

Instructor: Omer Bobrowski

Email: o|m|e|r|@|m|a|t|h|.|d|u|k|e|.|e|d|u

Office: Physics building #108

Office hours: By appointment

 

 

Synopsis:

 

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 ErdősRényi 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.

 

 

Grading:

 

Each registered student will choose a relevant topic/paper to study, and present it in class at the end of the semester.

 

 

Syllabus: HERE

Bibliography: HERE