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My research concerns unitary representations of Lie groups. In physical language, this means deciding what quantum-mechanical systems admit a given group of symmetries. I'm particularly interested in the "orbit method," which seeks to construct unitary representations by analogy with the (also ill-defined!) "quantization" for constructing quantum physical systems from classical ones.

In recent years I have been working with a group led by Jeff Adams , seeking to use computer calculations to understand these questions better.