The Vanderbilt University
Grant: $124,261 - National Science Foundation - Jun. 16, 2009
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Award Description: The theory of von Neumann algebras is a non-commutative integration theory which was _rst developed as a tool for understanding representation theory for groups as well as providing a mathematical framework for quantum mechanics. Recently the appearance of new rigidity phenomena in von Neumann algebras has led to deeper understanding and to the solutions to many longstanding problems both in von Neumann algebras and in other areas such as orbit equivalence ergodic theory and measurable equivalence relations. There has also emerged recently a connection between deformation/rigidity theory, free probablility, group cohomology, and derivations/quantum Dirichlet forms on von Neumann algebras. It is the intent of this author to investigate these new connections in order to gain more understanding of the relationship which is developing, and to use this understanding in order to approach some deep problems from new perspectives.
Project Description: The theory of von Neumann algebras is a non-commutative integration theory which was _rst developed as a tool for understanding representation theory for groups as well as providing a mathematical framework for quantum mechanics. Recently the appearance of new rigidity phenomena in von Neumann algebras has led to deeper understanding and to the solutions to many longstanding problems both in von Neumann algebras and in other areas such as orbit equivalence ergodic theory and measurable equivalence relations. There has also emerged recently a connection between deformation/rigidity theory, free probablility, group cohomology, and derivations/quantum Dirichlet forms on von Neumann algebras. It is the intent of this author to investigate these new connections in order to gain more understanding of the relationship which is developing, and to use this understanding in order to approach some deep problems from new perspectives.
Jobs Summary: The recovery act funds for this award helped to create or retain a type of position such as a professor. (Total jobs reported: 1)
Project Status: Less Than 50% Completed
This award's data was last updated on Jun. 16, 2009. Help expand these official descriptions using the wiki below.
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