We meet weekly for in-depth reading of papers and/or books in geometric functional analysis.

Geometric functional analysis can be described in two equivalent ways, analytic and geometric. The field was born as the analysis of Banach spaces in dimension n, where n grows to infinity. Equivalently, one can study convex symmetric sets in dimension n (unit balls of those Banach spaces), which explains connections of this field to convex geometry. Geometric functional analysis strives to understand and use high dimensional structures in mathematics. High dimensions often have srong regularization effect and help us to see the overall picture. While counter-intuitive, this is very similar to the methodology of probability theory. Taking more independent observations, we increase the dimension of the (product) probability space. As the dimension grows to infinity, the classical limit theorems such as the Central Limit Theorem begin to manifest themselves. The picture becomes simpler in higher than in lower dimensions. Techniques of geometric functional analysis are useful to explore, build, or use various high-dimensional structures such as Banach spaces, convex sets, matrices, signals and other massive data sets.

• Winter 2008: Dustin Mayeda was presenting "Elementary introduction into modern convex geometry" by K. Ball.
  
• Fall 2007: Worked on the survey "Euclidean structure in finite dimensional normed spaces" by A. Giannopoulos and V. Milman, in: Handbook of geometry of Banach spaces I, North-Holland, Amsterdam (2001), 707-779.
• Spring 2007: Worked on the notes on Concentration Inequalities by G. Lugosi.