Quantization on the affine group

Abstract: The classical notion of quantization in Euclidean space -- using time and frequency shifts -- has traditionally been of interest to people in classical analysis and theoretical physics. However, it has become more apparent in recent years that understanding geometric and algebraic aspects of quantization is essential. In this talk, I will review (a version of) classical quantization before moving on to the more recent phenomenon of quantization with time shifts and dilations. As probably suspected, this will naturally involve the affine group. I will show that the theory here is heavily influenced by the non-unimodularity of the affine group. If time permits, I will talk about some recent work and open problems that are left in this setting. The material presented is based on joint work with Stine M. Berge, Franz Luef, and Eirik Skrettingland.

functional analysisgroup theoryoperator algebrasquantum algebra

Audience: researchers in the topic

Groups, Operators, and Banach Algebras Webinar

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