Computer and Mathematical Sciences
Mathematical Structures I A01
KeywordsFoundations of quantum mechanics, Quantum Information Science, General Probabilistic Theories, Knot Theory, Low-dim Topology
Quantum Mechanics: Concepts and Mathematical Structures, Applications to Quantum Information Science. Research on knots and 3-dim manifolds
Research Overview of the Kimura Group:
Quantum mechanics is a fundamental theory of modern physics that describes the microscopic world of atoms and elementary particles, and it also underpins modern science and technology such as semiconductors and lasers. However, profound mysteries still remain in its interpretation and conceptual foundations, and there is no single unified view even among physicists. Taking Bell’s theorem --- which radically challenged our understanding of the nature of reality --- as one of our guiding themes, we study the meaning of observation, probability, correlation, and information that underlie quantum mechanics from both conceptual and mathematical physical perspectives. In particular, we aim to develop a broader and more unified understanding of quantum theory through the perspectives of open quantum systems and general probabilistic theories, while also exploring applications to quantum information science, including the principles of quantum communication and quantum computation.
Quantum mechanics is a fundamental theory of modern physics that describes the microscopic world of atoms and elementary particles, and it also underpins modern science and technology such as semiconductors and lasers. However, profound mysteries still remain in its interpretation and conceptual foundations, and there is no single unified view even among physicists. Taking Bell’s theorem --- which radically challenged our understanding of the nature of reality --- as one of our guiding themes, we study the meaning of observation, probability, correlation, and information that underlie quantum mechanics from both conceptual and mathematical physical perspectives. In particular, we aim to develop a broader and more unified understanding of quantum theory through the perspectives of open quantum systems and general probabilistic theories, while also exploring applications to quantum information science, including the principles of quantum communication and quantum computation.
Research Overview of the Bao Group:
I study knots and 3-dim manifolds, and my research topics include quantum invariants, Heegaard Floer homology etc. From a representation of a quantum group we can create an R-matrix, which is a solution to the Yang-Baxter equation. An R-matrix gives a matrix representation of braid group, and a quantum invariant is constructed in this way. Heegaard Floer homology is an invariant defined using techniques in symplectic geometry. I am interested in the topological applications and combinatorial interpretations of these invariants.
I study knots and 3-dim manifolds, and my research topics include quantum invariants, Heegaard Floer homology etc. From a representation of a quantum group we can create an R-matrix, which is a solution to the Yang-Baxter equation. An R-matrix gives a matrix representation of braid group, and a quantum invariant is constructed in this way. Heegaard Floer homology is an invariant defined using techniques in symplectic geometry. I am interested in the topological applications and combinatorial interpretations of these invariants.
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Our work ranges from foundational studies of the mysteries of quantum mechanics and its mathematical structure, including open quantum systems and general probability theory, to applications in quantum information science such as quantum communication, quantum computation, and quantum cryptography.
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Yang-Baxter equation