Discrete Geometry: Combinatorial Games and the Construction of the Surreal Numbers

Event Date: 

Wednesday, October 23, 2013 - 2:00pm to 3:00pm

Event Location: 

  • 4607B South Hall

Event Contact: 

Michael Dougherty

Email: dougherty@math.ucsb.edu

Speaker: Kyle Chapman

Abstract: Combinatorial Games are a class of games with perfect information and deterministic sequential play. This includes classics like Go and Chess as well as many others such as Nim and Dominering. The analysis of these games is extremely simple from a game theoretic standpoint, but the data analysis is extremely intense. Attempts to categorize these games has led to the construction of a proper class called the Surreal Numbers which have a group structure. The talk will go through this construction with the motivations tied to combinatorial games.