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Erlangen Program for \(\mathrm{SL}(2,\mathbb{Z}_p)\)

郑爽 Shuang Zheng

University of Leeds

Time: 16:00-18:00 (GMT+8), Monday March 27th, 2023
Location: Zoom

Abstract: The special linear group is the subgroup of a general linear group consisting of matrices with determinant \(1\) over a field or ring. Möbius transformations are naturally defined as the action of \(\mathrm{SL}(2,\mathbb{R})\) on a homogeneous space \(\mathrm{SL}(2,\mathbb{R})/H\) for some closed subgroup \(H\) of \(\mathrm{SL}(2,\mathbb{R})\). Cycles form a Möbius invariant family and parametrized either by quadratic form with a fixed signature or \(2\times 2\) matrices of a special form. This talk aims to discuss a similar theory by transferring the continuous idea of \(\mathrm{SL}(2,\mathbb{R})\) to the discrete case and investigate the quadratic forms over a discrete field or algebra (e.g., \(\mathrm{SL}(2,\mathbb{Z}_{p})\)) instead of the continuous plane.

Host: 谢贻林 Yilin Xie