School of Mathematics

Stein Structures: Existence and Flexibility

Kai Cieliebak
Ludwig-Maximilians-Universitat, Munich, Germany
February 29, 2012

This is a series of 3 talks on the topology of Stein manifolds, based on work of Eliashberg since the early 1990ies. More specifically, I wish to explain to what extent Stein structures are flexible, i.e. obey an h-principle. After providing some general background on Stein manifolds, the first talk will focus on the construction of plurisubharmonic functions with specific properties. Using these, I will in the second talk present the proof of Eliashberg's existence theorem for Stein structures.

Building Expanders in Three Steps

Amir Yehudayoff
Technion-Israel; Institute for Advanced Study
February 23, 2012
The talk will have 2 parts (between the parts we will have a break).

In the first part, we will discuss two options for using groups to construct expander graphs (Cayley graphs and Schreier diagrams). Specifically, we will see how to construct monotone expanders in this way. As in recent works (e.g. of Bourgain and Gamburd), we will see that the proof consists of 3 different steps. We will shortly discuss these 3 steps.

Zero Knowledge Proofs and Nuclear Disarmament

Boaz Barak
Microsoft Research New England
February 23, 2012
I'll describe a physical implementation of zero knowledge proofs whose goal is to verify that two physical objects are identical, without revealing any information about them. Our motivation is the task of verifying that an about-to-be-dismantled nuclear warhead is authentic without revealing its classified design. This is one of the technical hurdles that arises in implementing nuclear disarmament. I will not assume any background in either cryptography or nuclear disarmament.