"Tic-Tac-Toe theory -- an escape from the combinatorial chaos"
Abstract: I just finished a more-than-600-page long book (Tic-Tac-Toe theory) about combinatorial games, focusing on tic-tac-toe like games. In this talk I will discuss the main theorems and the main techniques in a rather informal way. I will attempt to answer basic questions like:
Part II: Tic-Tac-Toe theory -- results, proofs Monday, March 20th Math 110 11.00-13.00
Abstract: I will discuss the exciting connections and differences(!) between the so-called Probabilistic Method (``Erdos'') and the Fake Probabilistic Method (``potential technique''), the basic tool of this type of game theory. Why are games so much more challenging than the Random Model? What is the mysterious duality between Achievement and Avoidance games? I try to answer these questions. I will outline some proofs.
Abstract: I will mention the 10 most exciting open problems, and the partial results that we know about them (I will outline the proofs).