Algebraic invariants in mathematics and physics

  • Carey, Alan (PI)
  • Sukochev, Fedor A (CoI)

    Project: Research

    Project Details

    Description

    A remarkable development in modern physics has been the recognition that geometry and topology play an important role in fundamental theories of matter such as quantum mechanics. Recent revolutionary work of Alain Connes, motivated by problems of physical theory, has created a new mathematical theory, noncommutative geometry, with many applications in both mathematics and physics. We will extend this theory and its applications in novel directions resolving fundamental questions which limit the applications of Connes theory. We will generate new approaches to the mathematics of geometric and topological invariants via algebraic methods and provide new tools in quantum theory.
    StatusFinished
    Effective start/end date1/01/0831/12/11

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