TR 11-12:30 in 2-338.

Algorithmic problems in geometry often become tractable with the assumption of convexity (e.g. optimization, volume computation, learning, finding the average etc.). We will study this phenomenon in depth, beginning with classical topics such as the Brunn-Minkowski inequality and Gaussian isoperimetry, and then proceed to more recent developments in the field of geometric isoperimetric inequalities (e.g., if you cut a cylinder into two equal volume parts with a hyperplane, what is the minimum area of the separation? what is the maximum?), and their extensions to logconcave functions. One motivating problem will be that of efficiently sampling a geometric distribution by a random walk. Somewhat surprisingly, this problem plays a central role in the solution of all the algorithmic problems mentioned above.

A student taking the class for credit will
(1) Solve two problem sets.
(2) Scribe a lecture.
(3) Present a paper.
(4) (Optional) Work on a problem.

(3) and (4) can be done in groups of two students.