Tag - Combinatorial game theory

Joel David Hamkins: Infinite Games – Strategies, Logic, Theory, and Computation

16th June, 2023

Many familiar finite games admit natural infinitary analogues, which may captivate and challenge us with sublime complexity. Shall we have a game of infinite chess? Or how about infinite draughts, infinite Hex, infinite Wordle, or infinite Sudoku? In the Chocolatier’s game, the Chocolatier serves up an infinite stream of delicious morsels, while the Glutton aims to eat every one. These games and others illustrate the often subtle strategic aspects of infinite games, and sometimes their downright logical peculiarity. Does every infinite game admit of a winning strategy? Must optimal play be in principle computable? Let us discover the fascinating nature of infinitary strategic thinking.

Irit Dinur: High Dimensional Expanders and PCPs

31st January, 2017

I will describe a notion of high dimensional expansion called "agreement expansion", that can be described as a "sheaf cohomology". Agreement expansion captures certain PCP questions and in particular abstracts low degree tests such as plane vs. plane or line vs. line. 

I will then describe an agreement question on the finite-field Grassmannian which is a high dimensional version of the Raz-Safra plane vs. plane low degree test. We will discuss a hypothesis regarding agreement expansion on the Grassmannian. This hypothesis, if true, implies NP-hardness of 2:1 games, a variant of the unique games conjecture.