Hilbert's fifth problem and related topics
by Tao, Terence
fromGraduate studies in mathematics
In the fifth of his famous list of 23 problems, Hilbert asked if every topological group which was locally Euclidean was in fact a Lie group. Through the work of Gleason, Montgomery-Zippin, Yamabe, and others, this question was solved affirmatively; more generally, a satisfactor…
Expansion in finite simple groups of Lie type
by Tao, Terence
fromGraduate studies in mathematics
Expander graphs are an important tool in theoretical computer science, geometric group theory, probability, and number theory. Furthermore, the techniques used to rigorously establish the expansion property of a graph draw from such diverse areas of mathematics as representation…
This book offers a systematic treatment - the first in book form - of the development and use of cohomological induction to construct unitary representations. George Mackey introduced induction in 1950 as a real-analysis construction for passing from a unitary representation of …
We develop the structure theory of symplectic Lie groups based on the study of their isotropic normal subgroups. The article consists of three main parts. In the first part we show that every symplectic Lie group admits a sequence of subsequent symplectic reductions to a unique …