Genkai Zhang is working on representation theory of Lie groups and analysis on locally symmetric spaces. Much of the fundamental symmetries in mathematics and physics can be described in terms of Lie groups of transformations on geometric objects and their manifestations are studied using representations of Lie groups as matrices. Locally symmetric spaces are manifolds with large numbers of local symmetries. This research is mainly to understand the geometric and analytic properties of the spaces such as variations of their shapes, their resonance frequencies and quantum states, to discover and eventually classify unitary representations. Recently Genkai Zhang has been working on branching rules in representation theory, which is also called symmetry breaking in physics. Genkai Zhang has collabrations with colleagues in
Europe, China, Japan, South Korea and USA.
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