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SUMMARY:Lifting in special linear groups - Péter Varjú (University of Ca
 mbridge)
DTSTART:20250305T133000Z
DTEND:20250305T150000Z
UID:TALK227743@talks.cam.ac.uk
CONTACT:Julia Wolf
DESCRIPTION: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 pr
 oved 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 wi
 ll explain how this problem is related to bounding the diameter of the Ram
 anujan graphs of Lubotzky\, Phillips and Sarnak\, and to Sarnak's golden g
 ates in quantum computing. In the second half of the talk\, I will talk ab
 out the proof that the exponent 2 is best possible. This uses some tools f
 rom additive combinatorics.
LOCATION:MR4\, CMS
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