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Jason Hancox

Research student

Jason Hancox

Research overview

  • Noncommutative Probability
  • Quantum Groups
  • Functional Analysis

Research Interests

Noncommutative mathematics is an attempt at generalizing already existing mathematical objects in a satisfying and mathematically significant way. Loosely speaking, this is achieved by considering the algebra of complex valued functions on these objects with suitable structure and removing commutativity.

A short list of exceptional examples are C*-algebras, von Neumann algebras and compact quantum groups which correspond to locally compact Hausdorff topological space, sigma finite measure spaces and compact topological groups respectively.

I am currently investigating stochasic processes on quantum groups which include generalized notions of random walks and Lévy processes. Questions that are ever present include: "What properties from the well established classical theory can be translated over to this broader notion?" and "What results can be discovered from this abstract formulation that would not have been possible in the classical setting?". 

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