Description |
Infinite index subgroups of matrix groups like SL(n,Z) which are Zariski
dense in SL(n), arise in many geometric and diophantine problems (eg reflection groups, groups connected with elementary geometry such as integral apollonian packings, monodromy groups of families of algebraic varieties..). One of the key features needed for number theoretic
applications is that these groups obey some form of the Ramanujan Conjectures. In this context this asserts that certain congruence graphs associated with these groups are expanders. We will introduce these ideas and review some of the many recent developments.
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