Abstract: In this second talk we will discuss in more detail some recent results in the area of optimal stopping for the so called prophet secretary problem. In particular, we will note how "anonymity" and "adaptivity" play a crucial role in the design of effective algorithms for the problem. The plan is to cover:
1. An anonymous and adaptive algorithm that achieves a performance guarantee of 1-1/e.
2. A nonanonymous and nonadaptive algorithm with the same performance.
3. A nonanonymous and adaptive algorithm that beats the 1-1/e barrier.
4. An optimal adaptive algorithm for the special case of iid random variables.