MenuDouglas Lectures
Fall 2022
| Date: | November 1, 2022 |
| Time: | 4:00pm |
| Location: | BLOC 117 |
| Speaker: | Vern Paulsen |
| Title: | The Theory of Nonlocal Games and the problems of Tsirelson and Connes |
| Abstract: | Computer scientists have found ways to convert many tasks, such as determining if a system of equations has a solution, into games. When the players are allowed to access quantum entanglement, which is a nonlocal phenomenon, many games/tasks that have no classical solutions can be shown to have ``quantum'' solutions. This has led to the creation of new complexity classes in computer science and recently this complexity theory was used to prove that a long-standing problem in operator algebras, the Connes Embedding Problem(CEP), has a negative solution. In these talks we touch on many of these ideas and focus on the study of a family of these ``nonlocal'' games. We will show how the study of nonlocal games, without referring to complexity theory, leads to the negation of CEP. In Lecture 1, we will introduce the types of two person, cooperative games that we will be studying. We will discuss probabilistic strategies for games and quantum correlations. We will then introduce prover games that can be used to give probabilistic proofs that the players have solved certain types of problems. These include games for graph colourings, graph isomorphisms and games to determine if the players have solved a system of equations. This lecture should be broadly accessible. |
| Date: | November 2, 2022 |
| Time: | 4:00pm |
| Location: | BLOC 117 |
| Speaker: | Vern Paulsen |
| Title: | The Theory of Nonlocal Games and the problems of Tsirelson and Connes |
| Abstract: | In Lecture 2, we focus on synchronous quantum correlations and their relationship with traces on algebras. We derive a set of fundamental orthogonality relations that must be satisfied by an algebra to yield a perfect strategy and show how these results lead to a stronger refutation of Connes Embedding Problem. |
| Date: | November 3, 2022 |
| Time: | 4:00pm |
| Location: | BLOC 117 |
| Speaker: | Vern Paulsen |
| Title: | The Theory of Nonlocal Games and the problems of Tsirelson and Connes |
| Abstract: | In Lecture 3, we discuss the algebra of a game and how this can be used to prove that certain games that seem very different are in a certain sense equivalent. Time permitting, we will look at the topic of which model of quantum correlations best reflects the actual world and phenomena that separate these models. |
