Lifting in special linear groups
Ergodic Theory and Dynamical Systems Seminar
27th March 2025, 2:00 pm – 3:00 pm
Fry Building, 2.04
Given an element in SL_n(Z/qZ), what is the smallest element of SL_n(Z) that projects to it? We show that a lift with entries bounded by O(q^2 log q) always exists, and that the exponent 2 is best possible. Time permitting we may discuss the analogous problem of finding integer matrices with prescribed determinant that approximates a given matrix with real entries. Joint work with Amitay Kamber.
Organisers: Zemer Kosloff, David Parmenter
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