A nonlocal game is a two player co-operative game. In each round of the game, the verifier sends two questions, say x and y to the players, Alice and Bob. The players then reply with their answers, say a and b respectively. Whether or not Alice and Bob win this round of the game is given by the value of the predicate function V(a, b|x, y). What makes these games non-trivial is the fact that  Alice and Bob are not allowed to communicate during the game. 

  Alice and Bob can employ quantum strategies, where they make use of a shared entangled state. These quantum strategies can often given them an edge over classical strategies. Over the past few years, nonlocal games have been extensively studied and they have found applications in self-testing of quantum devices and quantum complexity theory.

  I have mostly worked on synchronous nonlocal games. Several of these synchronous nonlocal games are based on graphs. The  study of these nonlocal games involves a rich interplay of ideas from several fields such as quantum information, operator algebras, combinatorics and compact quantum groups. See the following entries on the papers section for more information:

• Robust Self-Testing for Synchronous Correlations and Games

• NPA Hierarchy for Quantum Isomorphism and Homomorphism Indistinguishability

• Transitive Nonlocal Games