**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 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.

**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