This topic brings together geometry, probability and complexity theory. Convex geometry, also called functional
analysis, studies phenomena in high dimension as the dimension tends to infinity. Over the past decade, algorithmic
questions have opened up exciting new directions in this classical field. In particular, understanding the complexity of
sampling and integration leads directly to concentration phenomena and the analysis of Markov chains in high dimension,
which in turn leads to the formulation of new isoperimetric inequalities. This will be a problem based talk attempting
to convey some of the central motivation of the field. A full graduate course will be offered in the Fall of 2008.