Lifting in special linear groups

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• Péter Varjú (University of Cambridge)
• Wednesday 05 March 2025, 13:30-15:00
• MR4, CMS.

If you have a question about this talk, please contact Julia Wolf.

Given an element in SL_n(Z/qZ), what is the smallest element of SL_n(Z) that projects to it? In a joint work with Amitay Kamber, we proved that a lift with entries bounded by O(q^2 log q) always exists, and that the exponent 2 is best possible. In the first half of the talk, I will explain how this problem is related to bounding the diameter of the Ramanujan graphs of Lubotzky, Phillips and Sarnak, and to Sarnak’s golden gates in quantum computing. In the second half of the talk, I will talk about the proof that the exponent 2 is best possible. This uses some tools from additive combinatorics.

This talk is part of the Discrete Analysis Seminar series.

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