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Research Interests
Research Interests
Nonlocal Games
Nonlocal Games
A nonlocal game involves two cooperating spatially separated players, Alice and Bob and a verifier. In each round of the game, the verifier picks two questions x and y and sends them to Alice and Bob respectively. If they respond with a and b respectively, then the verifier decides whether or not they win according to the predicate function V.
What makes these nonlocal games interesting is that players can gain a competitive advantage by using quantum strategies that use local measurements on a shared entangled state. I have worked on synchronous nonlocal games, which have several interesting interactions with operator algebras, quantum groups, and combinatorics.
Quantum Automorphism Groups of Graphs
Quantum Automorphism Groups of Graphs
Quantum automorphism groups of graphs arise as a natural non-commutative generalization of the notion of the automorphism group of a graph. I have worked on providing ways of explicitly calculating quantum automorphism groups of graphs. Our work is characterized by the use of combinatorial techniques like the Weisfeiler-Leman algorithm and making use of results about the graph isomorphism game.
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