An Introduction To Quantum Theory Keith Hannabuss Pdf Download |VERIFIED|
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One of the most important contributions to the theory of operator algebras and subfactors was the discovery of the Jones subfactor by Vaughan Jones. It was used in the classification of subfactors of index between four and five. Since that time, much effort has been spent trying to understand the general structure of these planar algebras, and it was one of the motivations in the development of the quantum group theory. Also, in the early 2000's, a breakthrough was achieved in the classification of subfactors. This classification classified all subfactors with index in the interval $[4,5]$ and also gave a detailed description of a subfactor with index value 5. More recently, there has been a lot of progress in the classification of subfactors of index $[5,6]$, and also the subfactors of index 5 that are not a group or a quantum group. The main obstacle to progress is the classification of subfactors with index $[5,6]$. One of the great questions in the theory is to classify subfactors with index value 6. Another open question is to understand the structure of subfactors with index values 4 and 5 in a natural and geometric way.
The programme is aimed at the young generation of operator algebraists, with strong background in linear algebra, in applications to quantum physics and with a taste for mathematics. The aim is to understand the mathematical foundations of operator algebras and subfactors and see the applications to the theory of quantum physics. The programme includes lectures and seminars on subjects such as subfactors of finite index, invariant theory for finite groups and their Lie algebras, projective representations of groups, quantum groups, co-amenability and subfactor planar algebras, using tools such as the double of a subfactor, the quantum double of a group, the Markov trace and the theory of corner algebras and planar algebras. Additional topics may include unbounded bimodules over subfactors, quantum walks and link invariants. There will be opportunities for attendees to present their own topics, perhaps on applications to quantum physics.
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